Question

If vector $2\hat{i}+3\hat{j}+8\hat{k}$ is perpendicular to the vector $4\hat{j}-4\hat{i}+\alpha \hat{k}$ , then the value of $\alpha$ is :-

• A. $-1$
• B. $\frac{1}{2}$
• C. $-\frac{1}{2}$
• D. $1$

Answer 1

The correct option is B $\frac{1}{2}$

Since they are perpendicular, thus dot product should be zero.
Thus, $(2\hat{i}+3\hat{j}+8\hat{k}).(4\hat{j}-4\hat{i}+\alpha \hat{k})=0$
$\Rightarrow 8-12+8\alpha =0$
$\Rightarrow 8\alpha =4$

Giving: $\alpha =\frac{1}{2}$