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Physics · WORK, ENERGY AND POWER

हिन्दी

In the vector representation shown in the figure, vector \( \mathbf{B} \) is inclined at an angle \( \theta \) to vector \( \mathbf{A} \). Which expression correctly gives the scalar product \( \mathbf{A} \cdot \mathbf{B} \) in terms of the components and projections illustrated?

Question diagram
  1. A
    \( A (B \cos\theta) = B (A \cos\theta) \)
  2. B
    \( B (A \tan\theta) \)
  3. C
    \( \frac{A}{B \cos\theta} \)
  4. D
    \( A (B \sin\theta) \)
View Answer & Solution

Correct answer · Option A

\( A (B \cos\theta) = B (A \cos\theta) \)

Explanation

Geometrically, the dot product equals the magnitude of \( \mathbf{A} \) multiplied by the projection of \( \mathbf{B} \) onto \( \mathbf{A} \) (\( B\cos\theta \)), or equivalently magnitude of \( \mathbf{B} \) times projection of \( \mathbf{A} \) onto \( \mathbf{B} \) (\( A\cos\theta \)).
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