First slide

Vectors

Question

The two vectors $\vec{A} = \hat{i} - 3 \hat{j} + y \hat{k}$ and $\vec{B} = \hat{i} + 2 \hat{j} + x \hat{k}$ are perpendicular. Find x y?

Moderate

A

5
B

2
C

3
D

4

Solution

$\vec{A} . \vec{B} {=A}_{x} B_{x} {+A}_{y} B_{y} {+A}_{z} B_{z} =0$
when the vectors are perpendicular.
$\vec{A} . \vec{B} =1-6+ x y =0$
$\Rightarrow x y = 5$

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