Dot product of any two perpendicular vector is zero.

(a) \( \vec{B} \times \vec{A} \cdot \vec{A} \)
(b) \( \vec{B} \cdot \vec{A} \cdot \vec{A} \)
(c) \( \vec{B} \cdot \vec{A} \cdot \vec{A} \neq \vec{C} \cdot \vec{A} \)
(d) \( \vec{B} \times \vec{A} \cdot \vec{A} = \vec{C} \cdot \vec{A} = CA \cos 90^\circ = 0 \)

Correct answer: (d) \( \vec{B} \times \vec{A} \cdot \vec{A} = \vec{C} \cdot \vec{A} = CA \cos 90^\circ = 0 \)

Solution

The dot product of two perpendicular vectors is zero because the cosine of the angle between them (90°) is zero. Option (d) correctly states this property and provides the mathematical reasoning.

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