The scalar product of two vectors A and B at an angle θ with each other is:
Correct answer: C. AB cos θ
- A. A B sin θ
- B. AB
- C. AB cos θ
- D. AB sec θ
Explanation
The scalar product, also known as the dot product, of two vectors A and B is calculated as |A||B| cos θ, where θ is the angle between the vectors. This formula combines the magnitudes of the vectors and the cosine of the angle between them. The cosine function reflects how much of one vector aligns with the direction of the other. Option A is incorrect because the sine function is used for the vector product, not the scalar product. Option B neglects the angle factor, which is crucial for the scalar product. Option D is incorrect because secant does not apply to this context.
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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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