Motion in a Plane - Result Question 7
9. If a 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) $1 / 2$
(c) 1
(b) $-1 / 2$
(d) -1
[2005]
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Answer:
Correct Answer: 9. (b)
Solution:
- (b) For two vectors to be perpendicular to each other
$\vec{A} \cdot \vec{B}=0$
$(2 \hat{i}+3 \hat{j}+8 \hat{k}) \cdot(4 \hat{j}-4 \hat{i}+\alpha \hat{k})=0$
$-8+12+8 \alpha=0$
$\alpha=-\frac{4}{8}=-\frac{1}{2}$
