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Sir in this question Prove that the vectors 3i+2j-2k,-i+3j+4k and 4i-j-6k can form a triangle. If we find the distance between the vectors and add them then we get zero so it is proved. But I cannot understand why do we find the distance between the vectors. Because these already represent vectors which form a triangle and I don't think these are the vertices. I think I have conceptual misunderstanding. Pls explain Thanks Jai

 
Sir in this question
Prove that the vectors 3i+2j-2k,-i+3j+4k and 4i-j-6k can form a triangle.
If we find the distance between the vectors and add them then we get zero so it is proved. 
But I cannot understand why do we find the distance between the vectors. Because these already represent vectors which form a triangle and I don't think these are the vertices.
I think I have conceptual misunderstanding.
Pls explain
Thanks
Jai

Grade:12

2 Answers

Yash Baheti IIT Roorkee
askIITians Faculty 97 Points
9 years ago
Hi,

Use the colinearity condition.
Three points must not be cloinear in order to form a triangle. The condition is the determinent is non zero if the vectors are forming a triangle.
So solve the determinent of three vectors and analyze the value.

The value to determinent is actually refers to area of triangle which will be zero if the triangle formation is not possible.

That is the proof.
Yash Baheti IIT Roorkee
askIITians Faculty 97 Points
9 years ago
Hi,

Use the colinearity condition.
Three points must not be cloinear in order to form a triangle. The condition is the determinent is non zero if the vectors are forming a triangle.
So solve the determinent of three vectors and analyze the value.

The value to determinent is actually refers to area of triangle which will be zero if the triangle formation is not possible.

That is the proof.

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