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

Hello Jai,
Whenever a question requires you to find whether the vectors form a triangle, the best and the simplest way is to use the triangle law of addition. If the vectors form a triangle they will obviously satisfy the triangle law of addition.
Here, we have (say)
A = 3i+2j-2k,
B = -i+3j+4k and
C = 4i-j-6k
Note that B + C = (-1 + 4)i + (3-1)j + (-6+4)k
= 3i + 2j - 2k
= A
Hence, since the sum of two vectors equals the third vector so the given vectors form a triangle.