How to find out the modulus of vectors in this question (as seen in the image):How to find the “average” direction of a set of vectors?Flux intergrals/Finding normals and their dot productsFind the equation of a plane when it passes through two points and parallel to two vectorsFind the direction in which the function $f(x, y)$ = $x^3y − x^2y^4$ decreases fastest at the point (5, −4).How to find the vector formula for the bisector of given two vectors?How to find the dot product inside of a squareFind the norm/magnitude of 2 cross products of vectorsHow to find the plane with given 2 vectors?How do I work with $2$D vectors where the origin is not at $(0, 0)$?For the question attached, how would you find the values of the vectors BA and BC?

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How to find out the modulus of vectors in this question (as seen in the image):


How to find the “average” direction of a set of vectors?Flux intergrals/Finding normals and their dot productsFind the equation of a plane when it passes through two points and parallel to two vectorsFind the direction in which the function $f(x, y)$ = $x^3y − x^2y^4$ decreases fastest at the point (5, −4).How to find the vector formula for the bisector of given two vectors?How to find the dot product inside of a squareFind the norm/magnitude of 2 cross products of vectorsHow to find the plane with given 2 vectors?How do I work with $2$D vectors where the origin is not at $(0, 0)$?For the question attached, how would you find the values of the vectors BA and BC?













0












$begingroup$


enter image description here



A problem I'm facing involves finding out the modulus of vectors. I understand that the modulus of a vector is the square of both the numbers and then the root of it to find the length. I was thinking for part (a) the answer would be 3 + (2*3) which is 9, and then the square root of this which will be 3. I used the same method to do part (b). However, I'm not sure whether what I have done is right, and I am stuck on part (c).










share|cite|improve this question









$endgroup$
















    0












    $begingroup$


    enter image description here



    A problem I'm facing involves finding out the modulus of vectors. I understand that the modulus of a vector is the square of both the numbers and then the root of it to find the length. I was thinking for part (a) the answer would be 3 + (2*3) which is 9, and then the square root of this which will be 3. I used the same method to do part (b). However, I'm not sure whether what I have done is right, and I am stuck on part (c).










    share|cite|improve this question









    $endgroup$














      0












      0








      0





      $begingroup$


      enter image description here



      A problem I'm facing involves finding out the modulus of vectors. I understand that the modulus of a vector is the square of both the numbers and then the root of it to find the length. I was thinking for part (a) the answer would be 3 + (2*3) which is 9, and then the square root of this which will be 3. I used the same method to do part (b). However, I'm not sure whether what I have done is right, and I am stuck on part (c).










      share|cite|improve this question









      $endgroup$




      enter image description here



      A problem I'm facing involves finding out the modulus of vectors. I understand that the modulus of a vector is the square of both the numbers and then the root of it to find the length. I was thinking for part (a) the answer would be 3 + (2*3) which is 9, and then the square root of this which will be 3. I used the same method to do part (b). However, I'm not sure whether what I have done is right, and I am stuck on part (c).







      vectors






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked 2 days ago









      V11V11

      196




      196




















          1 Answer
          1






          active

          oldest

          votes


















          2












          $begingroup$

          If $$b=2a$$ then we get $$|a+b|=|a+2a|=|3a|=3|a|$$



          If $$b=-2a$$ then we get $$3|-a|=3|a|$$



          If $a$ is perpendicular to $b$ then $$|a+b|^2=|a|^2+|b|^2=9+16=25$$ and $$|a+b|$$ gives $5$






          share|cite|improve this answer









          $endgroup$












          • $begingroup$
            Oh, thank you for your answer. However, just to make sure I understood the concept, I had a doubt. If b = -3a, wouldn't it become |a-3a| = |-2a|, which would then become -2|a|, resulting in -6 as the answer. The answer says 6 (I am not so sure of the rules of vectors like what would happen if the number is negative). Also, is there any rule that allows the two variables inside the modulus to be separated as done for part (c)? Thanks once again.
            $endgroup$
            – V11
            2 days ago










          • $begingroup$
            Note that $$|a-3a|=|-2a|=|-2||a|=2|a|$$
            $endgroup$
            – Dr. Sonnhard Graubner
            2 days ago










          • $begingroup$
            note that $$(a+b)cdot (a+b)=(a+b)^2=|a+b|^2$$ if $$cdot$$ means dot product.
            $endgroup$
            – Dr. Sonnhard Graubner
            2 days ago










          • $begingroup$
            Oh yes I get the second part. However, I didn't exactly understand how |−2||𝑎| would become 2|𝑎|.
            $endgroup$
            – V11
            2 days ago










          • $begingroup$
            We have this law also with real numbers and $$|-2|=2$$, by definition is it $$-(-2)=2$$
            $endgroup$
            – Dr. Sonnhard Graubner
            2 days ago











          Your Answer





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          1 Answer
          1






          active

          oldest

          votes








          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          2












          $begingroup$

          If $$b=2a$$ then we get $$|a+b|=|a+2a|=|3a|=3|a|$$



          If $$b=-2a$$ then we get $$3|-a|=3|a|$$



          If $a$ is perpendicular to $b$ then $$|a+b|^2=|a|^2+|b|^2=9+16=25$$ and $$|a+b|$$ gives $5$






          share|cite|improve this answer









          $endgroup$












          • $begingroup$
            Oh, thank you for your answer. However, just to make sure I understood the concept, I had a doubt. If b = -3a, wouldn't it become |a-3a| = |-2a|, which would then become -2|a|, resulting in -6 as the answer. The answer says 6 (I am not so sure of the rules of vectors like what would happen if the number is negative). Also, is there any rule that allows the two variables inside the modulus to be separated as done for part (c)? Thanks once again.
            $endgroup$
            – V11
            2 days ago










          • $begingroup$
            Note that $$|a-3a|=|-2a|=|-2||a|=2|a|$$
            $endgroup$
            – Dr. Sonnhard Graubner
            2 days ago










          • $begingroup$
            note that $$(a+b)cdot (a+b)=(a+b)^2=|a+b|^2$$ if $$cdot$$ means dot product.
            $endgroup$
            – Dr. Sonnhard Graubner
            2 days ago










          • $begingroup$
            Oh yes I get the second part. However, I didn't exactly understand how |−2||𝑎| would become 2|𝑎|.
            $endgroup$
            – V11
            2 days ago










          • $begingroup$
            We have this law also with real numbers and $$|-2|=2$$, by definition is it $$-(-2)=2$$
            $endgroup$
            – Dr. Sonnhard Graubner
            2 days ago
















          2












          $begingroup$

          If $$b=2a$$ then we get $$|a+b|=|a+2a|=|3a|=3|a|$$



          If $$b=-2a$$ then we get $$3|-a|=3|a|$$



          If $a$ is perpendicular to $b$ then $$|a+b|^2=|a|^2+|b|^2=9+16=25$$ and $$|a+b|$$ gives $5$






          share|cite|improve this answer









          $endgroup$












          • $begingroup$
            Oh, thank you for your answer. However, just to make sure I understood the concept, I had a doubt. If b = -3a, wouldn't it become |a-3a| = |-2a|, which would then become -2|a|, resulting in -6 as the answer. The answer says 6 (I am not so sure of the rules of vectors like what would happen if the number is negative). Also, is there any rule that allows the two variables inside the modulus to be separated as done for part (c)? Thanks once again.
            $endgroup$
            – V11
            2 days ago










          • $begingroup$
            Note that $$|a-3a|=|-2a|=|-2||a|=2|a|$$
            $endgroup$
            – Dr. Sonnhard Graubner
            2 days ago










          • $begingroup$
            note that $$(a+b)cdot (a+b)=(a+b)^2=|a+b|^2$$ if $$cdot$$ means dot product.
            $endgroup$
            – Dr. Sonnhard Graubner
            2 days ago










          • $begingroup$
            Oh yes I get the second part. However, I didn't exactly understand how |−2||𝑎| would become 2|𝑎|.
            $endgroup$
            – V11
            2 days ago










          • $begingroup$
            We have this law also with real numbers and $$|-2|=2$$, by definition is it $$-(-2)=2$$
            $endgroup$
            – Dr. Sonnhard Graubner
            2 days ago














          2












          2








          2





          $begingroup$

          If $$b=2a$$ then we get $$|a+b|=|a+2a|=|3a|=3|a|$$



          If $$b=-2a$$ then we get $$3|-a|=3|a|$$



          If $a$ is perpendicular to $b$ then $$|a+b|^2=|a|^2+|b|^2=9+16=25$$ and $$|a+b|$$ gives $5$






          share|cite|improve this answer









          $endgroup$



          If $$b=2a$$ then we get $$|a+b|=|a+2a|=|3a|=3|a|$$



          If $$b=-2a$$ then we get $$3|-a|=3|a|$$



          If $a$ is perpendicular to $b$ then $$|a+b|^2=|a|^2+|b|^2=9+16=25$$ and $$|a+b|$$ gives $5$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 2 days ago









          Dr. Sonnhard GraubnerDr. Sonnhard Graubner

          77.7k42866




          77.7k42866











          • $begingroup$
            Oh, thank you for your answer. However, just to make sure I understood the concept, I had a doubt. If b = -3a, wouldn't it become |a-3a| = |-2a|, which would then become -2|a|, resulting in -6 as the answer. The answer says 6 (I am not so sure of the rules of vectors like what would happen if the number is negative). Also, is there any rule that allows the two variables inside the modulus to be separated as done for part (c)? Thanks once again.
            $endgroup$
            – V11
            2 days ago










          • $begingroup$
            Note that $$|a-3a|=|-2a|=|-2||a|=2|a|$$
            $endgroup$
            – Dr. Sonnhard Graubner
            2 days ago










          • $begingroup$
            note that $$(a+b)cdot (a+b)=(a+b)^2=|a+b|^2$$ if $$cdot$$ means dot product.
            $endgroup$
            – Dr. Sonnhard Graubner
            2 days ago










          • $begingroup$
            Oh yes I get the second part. However, I didn't exactly understand how |−2||𝑎| would become 2|𝑎|.
            $endgroup$
            – V11
            2 days ago










          • $begingroup$
            We have this law also with real numbers and $$|-2|=2$$, by definition is it $$-(-2)=2$$
            $endgroup$
            – Dr. Sonnhard Graubner
            2 days ago

















          • $begingroup$
            Oh, thank you for your answer. However, just to make sure I understood the concept, I had a doubt. If b = -3a, wouldn't it become |a-3a| = |-2a|, which would then become -2|a|, resulting in -6 as the answer. The answer says 6 (I am not so sure of the rules of vectors like what would happen if the number is negative). Also, is there any rule that allows the two variables inside the modulus to be separated as done for part (c)? Thanks once again.
            $endgroup$
            – V11
            2 days ago










          • $begingroup$
            Note that $$|a-3a|=|-2a|=|-2||a|=2|a|$$
            $endgroup$
            – Dr. Sonnhard Graubner
            2 days ago










          • $begingroup$
            note that $$(a+b)cdot (a+b)=(a+b)^2=|a+b|^2$$ if $$cdot$$ means dot product.
            $endgroup$
            – Dr. Sonnhard Graubner
            2 days ago










          • $begingroup$
            Oh yes I get the second part. However, I didn't exactly understand how |−2||𝑎| would become 2|𝑎|.
            $endgroup$
            – V11
            2 days ago










          • $begingroup$
            We have this law also with real numbers and $$|-2|=2$$, by definition is it $$-(-2)=2$$
            $endgroup$
            – Dr. Sonnhard Graubner
            2 days ago
















          $begingroup$
          Oh, thank you for your answer. However, just to make sure I understood the concept, I had a doubt. If b = -3a, wouldn't it become |a-3a| = |-2a|, which would then become -2|a|, resulting in -6 as the answer. The answer says 6 (I am not so sure of the rules of vectors like what would happen if the number is negative). Also, is there any rule that allows the two variables inside the modulus to be separated as done for part (c)? Thanks once again.
          $endgroup$
          – V11
          2 days ago




          $begingroup$
          Oh, thank you for your answer. However, just to make sure I understood the concept, I had a doubt. If b = -3a, wouldn't it become |a-3a| = |-2a|, which would then become -2|a|, resulting in -6 as the answer. The answer says 6 (I am not so sure of the rules of vectors like what would happen if the number is negative). Also, is there any rule that allows the two variables inside the modulus to be separated as done for part (c)? Thanks once again.
          $endgroup$
          – V11
          2 days ago












          $begingroup$
          Note that $$|a-3a|=|-2a|=|-2||a|=2|a|$$
          $endgroup$
          – Dr. Sonnhard Graubner
          2 days ago




          $begingroup$
          Note that $$|a-3a|=|-2a|=|-2||a|=2|a|$$
          $endgroup$
          – Dr. Sonnhard Graubner
          2 days ago












          $begingroup$
          note that $$(a+b)cdot (a+b)=(a+b)^2=|a+b|^2$$ if $$cdot$$ means dot product.
          $endgroup$
          – Dr. Sonnhard Graubner
          2 days ago




          $begingroup$
          note that $$(a+b)cdot (a+b)=(a+b)^2=|a+b|^2$$ if $$cdot$$ means dot product.
          $endgroup$
          – Dr. Sonnhard Graubner
          2 days ago












          $begingroup$
          Oh yes I get the second part. However, I didn't exactly understand how |−2||𝑎| would become 2|𝑎|.
          $endgroup$
          – V11
          2 days ago




          $begingroup$
          Oh yes I get the second part. However, I didn't exactly understand how |−2||𝑎| would become 2|𝑎|.
          $endgroup$
          – V11
          2 days ago












          $begingroup$
          We have this law also with real numbers and $$|-2|=2$$, by definition is it $$-(-2)=2$$
          $endgroup$
          – Dr. Sonnhard Graubner
          2 days ago





          $begingroup$
          We have this law also with real numbers and $$|-2|=2$$, by definition is it $$-(-2)=2$$
          $endgroup$
          – Dr. Sonnhard Graubner
          2 days ago


















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