Show that $a,b,c$ forms the sides of a triangle. Please help on my attempt. The 2019 Stack Overflow Developer Survey Results Are InIs it possible to have triangle other than equilateral of which sum of two sides = twice the other side?Find the probability that splitting the unit interval into three random segments results in the sides of a triangle.Show that it is not possible to have a triangle with sides $a,b,c$$ldots$Sides of a triangle (square roots)?Euclidean geometry please help meLet $a,b,c$ be the lenghts of the sides of a triangle. Suppose that $ab+bc+ca=1$. Show that $(a+1)(b+1)(c+1)<4$Rewrite sides of triangle$triangle ABC$ and $triangle ADE$ are isosceles. Show that $angle BAD=angle EAC$Please help me with this cone question.Using vector operations, Prove the line segment joining the midpoints of two sides of a triangle
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Show that $a,b,c$ forms the sides of a triangle. Please help on my attempt.
The 2019 Stack Overflow Developer Survey Results Are InIs it possible to have triangle other than equilateral of which sum of two sides = twice the other side?Find the probability that splitting the unit interval into three random segments results in the sides of a triangle.Show that it is not possible to have a triangle with sides $a,b,c$$ldots$Sides of a triangle (square roots)?Euclidean geometry please help meLet $a,b,c$ be the lenghts of the sides of a triangle. Suppose that $ab+bc+ca=1$. Show that $(a+1)(b+1)(c+1)<4$Rewrite sides of triangle$triangle ABC$ and $triangle ADE$ are isosceles. Show that $angle BAD=angle EAC$Please help me with this cone question.Using vector operations, Prove the line segment joining the midpoints of two sides of a triangle
$begingroup$
Show that $a=2i+2j+3k,b=3i+j-k,c=i-j-4k$ forms the sides of a triangle.
My attempt: $|a|=sqrt17,|b|=sqrt11,|c|=sqrt18.$ Since $|c|<|a|+|b|$ using triangle inequality, we can say $a,b,c$ form sides of a triangle.
I am not sure if my attempt is correct. Please help.
geometry vector-spaces vectors
asked Mar 24 at 5:35
JaveJave
496214
$endgroup$
add a comment |
$begingroup$
Show that $a=2i+2j+3k,b=3i+j-k,c=i-j-4k$ forms the sides of a triangle.
My attempt: $|a|=sqrt17,|b|=sqrt11,|c|=sqrt18.$ Since $|c|<|a|+|b|$ using triangle inequality, we can say $a,b,c$ form sides of a triangle.
I am not sure if my attempt is correct. Please help.
geometry vector-spaces vectors
asked Mar 24 at 5:35
JaveJave
496214
$endgroup$
add a comment |
$begingroup$
Show that $a=2i+2j+3k,b=3i+j-k,c=i-j-4k$ forms the sides of a triangle.
My attempt: $|a|=sqrt17,|b|=sqrt11,|c|=sqrt18.$ Since $|c|<|a|+|b|$ using triangle inequality, we can say $a,b,c$ form sides of a triangle.
I am not sure if my attempt is correct. Please help.
geometry vector-spaces vectors
asked Mar 24 at 5:35
JaveJave
496214
$endgroup$
Show that $a=2i+2j+3k,b=3i+j-k,c=i-j-4k$ forms the sides of a triangle.
My attempt: $|a|=sqrt17,|b|=sqrt11,|c|=sqrt18.$ Since $|c|<|a|+|b|$ using triangle inequality, we can say $a,b,c$ form sides of a triangle.
I am not sure if my attempt is correct. Please help.
geometry vector-spaces vectors
geometry vector-spaces vectors
asked Mar 24 at 5:35
JaveJave
496214
asked Mar 24 at 5:35
JaveJave
496214
edited Mar 24 at 5:42
Jave
asked Mar 24 at 5:35
JaveJave
496214
asked Mar 24 at 5:35
JaveJave
496214
asked Mar 24 at 5:35
JaveJave
496214
496214
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
In the vector form it is necessary to check the directions. By the triangle law of vector addition , the sum of vectors (in either of direction)should be zero. Then they are guaranteed to be sides of a triangle,then no need to check length or any other conditions. Also your method is not a proof. You can see here $vec a + vec c= vec b$ or $vec a + vec c +(-vec b) = vec 0$ .
answered Mar 24 at 5:50
TojrahTojrah
4036
$endgroup$
$begingroup$
$vec a + vec b + (-vec c) ne 0$, but $vec a + vec c + (-vec b) = 0$.
$endgroup$
– Toby Mak
Mar 24 at 5:58
$begingroup$
Just corrected:)
$endgroup$
– Tojrah
Mar 24 at 6:02
add a comment |
$begingroup$
To use the triangle inequality, you need to show the sum of any two sides is greater than the third side. Therefore, you also need to verify:
$$|a| ≤ |b| + |c|$$
$$|b| ≤ |c| + |a|$$
answered Mar 24 at 5:45
Toby MakToby Mak
3,57511128
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
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active
oldest
votes
$begingroup$
In the vector form it is necessary to check the directions. By the triangle law of vector addition , the sum of vectors (in either of direction)should be zero. Then they are guaranteed to be sides of a triangle,then no need to check length or any other conditions. Also your method is not a proof. You can see here $vec a + vec c= vec b$ or $vec a + vec c +(-vec b) = vec 0$ .
answered Mar 24 at 5:50
TojrahTojrah
4036
$endgroup$
$begingroup$
$vec a + vec b + (-vec c) ne 0$, but $vec a + vec c + (-vec b) = 0$.
$endgroup$
– Toby Mak
Mar 24 at 5:58
$begingroup$
Just corrected:)
$endgroup$
– Tojrah
Mar 24 at 6:02
add a comment |
$begingroup$
In the vector form it is necessary to check the directions. By the triangle law of vector addition , the sum of vectors (in either of direction)should be zero. Then they are guaranteed to be sides of a triangle,then no need to check length or any other conditions. Also your method is not a proof. You can see here $vec a + vec c= vec b$ or $vec a + vec c +(-vec b) = vec 0$ .
answered Mar 24 at 5:50
TojrahTojrah
4036
$endgroup$
$begingroup$
$vec a + vec b + (-vec c) ne 0$, but $vec a + vec c + (-vec b) = 0$.
$endgroup$
– Toby Mak
Mar 24 at 5:58
$begingroup$
Just corrected:)
$endgroup$
– Tojrah
Mar 24 at 6:02
add a comment |
$begingroup$
In the vector form it is necessary to check the directions. By the triangle law of vector addition , the sum of vectors (in either of direction)should be zero. Then they are guaranteed to be sides of a triangle,then no need to check length or any other conditions. Also your method is not a proof. You can see here $vec a + vec c= vec b$ or $vec a + vec c +(-vec b) = vec 0$ .
answered Mar 24 at 5:50
TojrahTojrah
4036
$endgroup$
In the vector form it is necessary to check the directions. By the triangle law of vector addition , the sum of vectors (in either of direction)should be zero. Then they are guaranteed to be sides of a triangle,then no need to check length or any other conditions. Also your method is not a proof. You can see here $vec a + vec c= vec b$ or $vec a + vec c +(-vec b) = vec 0$ .
answered Mar 24 at 5:50
TojrahTojrah
4036
edited Mar 24 at 6:02
answered Mar 24 at 5:50
TojrahTojrah
4036
answered Mar 24 at 5:50
TojrahTojrah
4036
answered Mar 24 at 5:50
TojrahTojrah
4036
4036
$begingroup$
$vec a + vec b + (-vec c) ne 0$, but $vec a + vec c + (-vec b) = 0$.
$endgroup$
– Toby Mak
Mar 24 at 5:58
$begingroup$
Just corrected:)
$endgroup$
– Tojrah
Mar 24 at 6:02
add a comment |
$begingroup$
$vec a + vec b + (-vec c) ne 0$, but $vec a + vec c + (-vec b) = 0$.
$endgroup$
– Toby Mak
Mar 24 at 5:58
$begingroup$
Just corrected:)
$endgroup$
– Tojrah
Mar 24 at 6:02
$begingroup$
$vec a + vec b + (-vec c) ne 0$, but $vec a + vec c + (-vec b) = 0$.
$endgroup$
– Toby Mak
Mar 24 at 5:58
$begingroup$
$vec a + vec b + (-vec c) ne 0$, but $vec a + vec c + (-vec b) = 0$.
$endgroup$
– Toby Mak
Mar 24 at 5:58
$begingroup$
Just corrected:)
$endgroup$
– Tojrah
Mar 24 at 6:02
$begingroup$
Just corrected:)
$endgroup$
– Tojrah
Mar 24 at 6:02
add a comment |
$begingroup$
To use the triangle inequality, you need to show the sum of any two sides is greater than the third side. Therefore, you also need to verify:
$$|a| ≤ |b| + |c|$$
$$|b| ≤ |c| + |a|$$
answered Mar 24 at 5:45
Toby MakToby Mak
3,57511128
$endgroup$
add a comment |
$begingroup$
To use the triangle inequality, you need to show the sum of any two sides is greater than the third side. Therefore, you also need to verify:
$$|a| ≤ |b| + |c|$$
$$|b| ≤ |c| + |a|$$
answered Mar 24 at 5:45
Toby MakToby Mak
3,57511128
$endgroup$
add a comment |
$begingroup$
To use the triangle inequality, you need to show the sum of any two sides is greater than the third side. Therefore, you also need to verify:
$$|a| ≤ |b| + |c|$$
$$|b| ≤ |c| + |a|$$
answered Mar 24 at 5:45
Toby MakToby Mak
3,57511128
$endgroup$
To use the triangle inequality, you need to show the sum of any two sides is greater than the third side. Therefore, you also need to verify:
$$|a| ≤ |b| + |c|$$
$$|b| ≤ |c| + |a|$$
answered Mar 24 at 5:45
Toby MakToby Mak
3,57511128
answered Mar 24 at 5:45
Toby MakToby Mak
3,57511128
answered Mar 24 at 5:45
Toby MakToby Mak
3,57511128
answered Mar 24 at 5:45
Toby MakToby Mak
3,57511128
3,57511128
add a comment |
add a comment |
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