Asked in Premeth — Coordination and Control, Vectors and EquilibriumModerate

A is parallel to B then A.B =

Correct answer: B. AB

  • A. zero
  • B. AB
  • C. -AB
  • D. A/b
  • E. none

Explanation

The dot product of two vectors A and B is given by the formula A·B = |A| |B| cos(θ), where θ is the angle between the vectors. For parallel vectors, θ = 0°. The cosine of 0° is 1, so the dot product simplifies to |A| |B|, or AB.Option A is incorrect because a dot product of zero indicates perpendicular vectors, not parallel ones. Option C is incorrect as it suggests a negative product which would apply if the vectors were anti-parallel. Option D is not a valid mathematical expression for a dot product. Option E is incorrect as the dot product for parallel vectors is not 'none'.

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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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