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The dot product of two vectors is

  • A.a vector whose magnitude is the area of the parallelogram they define
  • B.a scalar equal to the product of their magnitudes and the cosine of the angle between them
  • C.a vector perpendicular to both of the vectors being multiplied together
  • D.a scalar equal to the product of their magnitudes and the sine of the angle

Answer: B

Correct answer: a scalar equal to the product of their magnitudes and the cosine of the angle between them

\[ \mathbf{A}\cdot\mathbf{B} = AB\cos\theta. \] The result is a number, not a vector, and it measures how much of one vector lies along the other - which is why it appears wherever a projection or a component is wanted, as in work done or flux through a surface.

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