First slide

Vectors

Question

If $\vec{A} and \vec{B}$ are perpendicular vectors and vector $\vec{A} = 5 \hat{i} + 7 \hat{j} - 3 \hat{k} and \vec{B} = 2 \hat{i} + 2 \hat{j} - a \hat{k}$ . The value of a is

Moderate

A

-2
B

8
C

-7
D

-8

Solution

For perpendicular vector $\vec{A} . \vec{B} = 0$
$\Rightarrow (5 \hat{i} + 7 \hat{j} - 3 \hat{k}) . (2 \hat{i} + 2 \hat{j} - a \hat{k}) = 0$
$\Rightarrow 10 + 14 + 3 a = 0 \Rightarrow a = - 8$

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