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Physics · WORK, ENERGY AND POWER
हिन्दीTwo vectors are given by \( \mathbf{A} = 2\hat{\mathbf{i}} + 3\hat{\mathbf{j}} - p\hat{\mathbf{k}} \) and \( \mathbf{B} = 4\hat{\mathbf{i}} - 2\hat{\mathbf{j}} + 2\hat{\mathbf{k}} \). If the vectors \( \mathbf{A} \) and \( \mathbf{B} \) are perpendicular to each other, the magnitude of the projection of vector \( \mathbf{A} \) on the vector \( \mathbf{C} = 2\hat{\mathbf{i}} + 2\hat{\mathbf{j}} - \hat{\mathbf{k}} \) is:
Correct answer · Option 3
\( 3 \text{ units} \)
Explanation
Since \( \mathbf{A} \cdot \mathbf{B} = 0 \), \( 8 - 6 - 2p = 0 \implies p = 1 \). Then \( \mathbf{A} = 2\hat{\mathbf{i}} + 3\hat{\mathbf{j}} - \hat{\mathbf{k}} \). Projection on \( \mathbf{C} \) is \( \frac{\mathbf{A} \cdot \mathbf{C}}{|\mathbf{C}|} = \frac{4 + 6 + 1}{\sqrt{4+4+1}} = \frac{9}{3} = 3 \).
