First slide

Vectors

Question

The two vectors $\vec{A} = - 2 \hat{i} + 3 \hat{j} + y \hat{k}$ and $\vec{B} = \hat{i} + 2 \hat{j} + x \hat{k}$ are perpendicular. Given $x + y = 0$ . Find x and y?

Moderate

A

$x = 2 a n d y = - 1$
B

$x = 2 a n d y = - 2$
C

$x = 1 a n d y = - 2$
D

$x = 1 a n d y = - 1$

Solution

$x + y = 0$
when the vectors are perpendicular.
$\vec{A} . \vec{B} {=A}_{x} B_{x} {+A}_{y} B_{y} {+A}_{z} B_{z} =0$
$\vec{A} . \vec{B} =-2+6+ x y =0$
$\Rightarrow x y = - 4$
${(x - y)}^{2} = {(x + y)}^{2} - 4 x y$
$x - y = \pm 4$
$x = 2 a n d y = - 2$
or $x = - 2 a n d y = 2$

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