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