Question

Which of the following is NOT true about vectors \( \vec{A}, \vec{B}, \vec{C} \)?

• A. \( (\vec{A} \cdot \vec{A}), (\vec{B} \cdot \vec{C}) \) are scalar values
• B. \( (\vec{A} \cdot \vec{B})(\vec{B} \cdot \vec{C}) \) is a scalar value
• C. \( (\vec{A} \cdot \vec{C})(\vec{B} \cdot \vec{C}) \) is a scalar value
• D. \( \vec{A} \times (\vec{B} \cdot \vec{C}) \) is a vector value

Hint:

Dot product gives scalar, cross product gives vector; can’t cross a scalar with a vector.

Answer 1

The Correct Option is D

\( \vec{B} \cdot \vec{C} \) is a scalar, and cross product requires both operands to be vectors. So \( \vec{A} \times (\vec{B} \cdot \vec{C}) \) is invalid — not a vector, but undefined.