Angle that the vector A =2 i +2 j makes with y-axis is: - Vidyadip

MCQ

Angle that the vector $\vec{\text{A}}=2\hat{\text{i}}+2\hat{\text{j}}$ makes with $y-$axis is:

A
$\tan^{-1}\Big(\frac{3}{2}\Big)$
✓
$\tan^{-1}\Big(\frac{2}{3}\Big)$
C
$\sin^{-1}\Big(\frac{2}{3}\Big)$
D
$\cos^{-1}\Big(\frac{3}{2}\Big)$

✓

Answer

Correct option: B.

$\tan^{-1}\Big(\frac{2}{3}\Big)$

As $\vec{\text{A}}=2\hat{\text{i}}+2\hat{\text{j}},$
therefore $A_x = 2$ and $A_y = 3.$ If $\theta$ is the angle which $\vec{\text{A}}$ encloses with $y-$axis, then.
$\tan\theta=\frac{\text{A}_\text{x}}{\text{A}_\text{y}}=\frac{2}{3}$ or $\theta=\tan^{-1}\Big(\frac{2}{3}\Big)$

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