Question

The given vectors can form sides of a triangle $\hat{i}-\hat{j}-\hat{k},-2\hat{i}+3\hat{j}-\hat{k},\hat{i}-2\hat{j}+2\hat{k}$

• A. True
• B. False

Answer 1

The correct option is A

True

First we have to check if the vectors are collinear. Clearly they are not as you cannot represent one vector as a scalar multiple of any other. Next we will check if sum of them is 0.

$(\hat{i}-\hat{j}-\hat{k})+(-2\hat{i}+3\hat{j}-\hat{k})+(\hat{i}-2\hat{j}+2\hat{k})$

$=0\hat{i}+0\hat{j}+0\hat{k}=0$

They do satisfy the triangle law but with one of the vectors in negative direction which shouldn’t be effecting the possibility of forming a triangle.

$\therefore$The vectors can from the sides of a triangle.