Question

# If the vectors $$\displaystyle \vec{P}= a\tilde{i}+a\hat{j}+3\hat{k}\:and\:\vec{Q}= a\hat{i}-2\hat{j}-\hat{k}$$ are perpendicular to each other then the positive value of a is

A
zero
B
1
C
2
D
3

Solution

## The correct option is B 3Given, perpendicular, implies $$\vec{P}.\vec{Q}=0$$or, $$(a\hat{i}+a\hat{j}+3\hat{k}).(a\hat{i}-2\hat{j}-\hat{k})=0$$or, $${a}^{2}-2a-3=0$$Solving the quadratic, we get, $$a=3$$ or $$-1$$. Positive value is thus $$3$$.Physics

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