Question

Find the value of m so that the vector 3$\hat{i}-2\hat{j}+\hat{k}$ may be perpendicular to the vector $2\hat{i}+6\hat{j}+m\hat{k}$.

• A. m = 2
• B. m = 3
• C. m = 5
• D. m = 6

Answer 1

The correct option is D

m = 6

The given vectors will be perpendicular if their dot product is zero.

$3\hat{i}-2\hat{j}+\hat{k}$ . $2\hat{i}+6\hat{j}+m\hat{k}$ = 0

6$(\hat{i}.\hat{j})-12(\hat{j}.\hat{j})+m(\hat{k}.\hat{k})=0$

Or, 6 - 12 + m = 0 or, m - 6 = 0, or m = 6