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Physics · MOTION IN A PLANE
हिन्दीA vector \( \mathbf{A} = 2\hat{\mathbf{i}} + 2\sqrt{3}\hat{\mathbf{j}} \) is rotated counter-clockwise about the origin by an angle of \( 30^\circ \) in the x-y plane to obtain a new vector \( \mathbf{B} \). Express vector \( \mathbf{B} \) in component form.
Correct answer · Option 1
\( 4\hat{\mathbf{j}} \)
Explanation
The magnitude is \( |\mathbf{A}| = \sqrt{2^2 + (2\sqrt{3})^2} = 4 \). Initial angle with x-axis is \( \theta_1 = \tan^{-1}(\sqrt{3}) = 60^\circ \). Rotating counter-clockwise by \( 30^\circ \) gives \( \theta_2 = 90^\circ \). Thus \( \mathbf{B} = 4\hat{\mathbf{j}} \).
