If A=B, which of the following is not correct ?
Correct answer: A. A.B = A^ B^
- A. A.B = A^ B^
- B. |A| = |B|
- C. |A^| = |B^|
- D. AB^ = BA^
Explanation
If A and B are equal vectors, then their magnitudes and unit vectors are equal, and A B-hat = B A-hat also remains equal. However, A·B = |A||B| cos θ, whereas A-hat·B-hat = cos θ, so these are not generally equal unless |A||B| = 1. Students may choose b because it is a direct consequence of equal vectors, but a is the incorrect statement.
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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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