Asked in Premeth — Coordination and Control, Vectors and Equilibrium

If A.B = 0, we conclude that:

Correct answer: D. All of the above

  • A. Either of two vectors is a null vector
  • B. Both of the vectors are null vectors
  • C. The vectors are mutually perpendicular
  • D. All of the above

Explanation

The correct option is (d) - if A.B = 0, we can conclude that all of the options are true. Let's go through each option and explain them:(a) Either of two vectors is a null vector: A null vector is a vector with zero magnitude. If the dot product of two vectors is zero, it means that at least one of the vectors has to be a null vector. This option is true.(b) Both of the vectors are null vectors: While it is possible for both vectors to be null vectors, it is not the only possibility. If the dot product of two vectors is zero, it means that at least one of the vectors has to be a null vector, but the other vector can have a non-zero magnitude. So, this option is not always true.(c) The vectors are mutually perpendicular: When the dot product of two vectors is zero, it means that the vectors are orthogonal or perpendicular to each other. So, this option is true.(d) All of the above: If A.B = 0, it means that either of the vectors is a null vector, both vectors can be null vectors, and the vectors are mutually perpendicular. So, all of the options are true.In summary, if the dot product of two vectors is zero, we can conclude that either of the vectors is a null vector, both vectors can be null vectors, and the vectors are mutually perpendicular.

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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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