The scalar product of two vectors A and B is defined as
Correct answer: B. AB cos theta, and the result is a scalar
- A. AB sin theta, and the result is a vector
- B. AB cos theta, and the result is a scalar
- C. AB tan theta, and the result is a scalar
- D. AB, independent of the angle between them
Explanation
The dot product multiplies the magnitudes by the cosine of the angle between the vectors and gives a scalar, which is why work, the dot product of force and displacement, is a scalar. The sine form belongs to the vector product, whose result is a vector. The cosine factor is what makes the dot product zero for perpendicular vectors.
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About Scalar Product
The scalar product of two vectors is A dot B equals AB cos theta, producing a scalar determined by their magnitudes and included angle. Applications include work done and projection of one vector on another, with perpendicular vectors giving zero and the scalar product distinguished from the vector product.
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