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Motion in a Plane — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsMotion in a Plane1 Mark
MCQ
Angle that the vector $\vec{\text{A}}=2\hat{\text{i}}+2\hat{\text{j}}$ makes with y-axis is:
  • A
    $\tan^{-1}\Big(\frac{3}{2}\Big)$
  • B
    $\tan^{-1}\Big(\frac{2}{3}\Big)$
  • C
    $\sin^{-1}\Big(\frac{2}{3}\Big)$
  • D
    $\cos^{-1}\Big(\frac{3}{2}\Big)$
✓

Answer

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

Explanation:

As $\vec{\text{A}}=2\hat{\text{i}}+2\hat{\text{j}},$ therefore Ax = 2 and Ay = 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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