If A=Ax i^ + Ay j^ + Az K^ B = Bx i^ + By j^ + Bz K^ then______________?
Correct answer: A. A. B = Ax Bx + Ay By + Az Bz
- A. A. B = Ax Bx + Ay By + Az Bz
- B. A. B = Ax By + Ay Bz + Az By
- C. A. B = Ay Bz + Az By + Az Bx
- D. A. B = Ax Bz + Ay By + Az Bx
Explanation
The dot product multiplies corresponding components and then adds them: A · B = AxBx + AyBy + AzBz. The other expressions mix non-corresponding components and do not represent the scalar product. Option b is the likely distractor because it still contains component symbols but pairs them incorrectly.
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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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