First slide

Vectors

Question

${\hat{e}}_{r} is unit vector along radius of a circle shown in figure . {\hat{e}}_{r} can be represented as$

Moderate

A

$cosθ \hat{i} + sinθ \hat{j}$
B

$sinθ \hat{i} + cosθ \hat{j}$
C

$cosθ \hat{i} - sinθ \hat{j}$
D

$- cosθ \hat{i} + sinθ \hat{j}$

Solution

The component of ${\hat{e}}_{r}$ along X-axis is
${\hat{e}}_{r} cosθ = 1 \times cosθ = cosθ$
The component of ${\hat{e}}_{r}$ along Y-axis is
${\hat{e}}_{r} sinθ = 1 \times sinθ = sinθ$
$∴ {\hat{e}}_{r} = cosθ \hat{i} + sinθ \hat{j}$

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