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If the resultant of \(\vec{A}=6\hat{A}\) and \(\vec{B}=8\hat{B}\) is \(\vec{R}=10\hat{R}\) where \(\hat{A},\hat{B}\) and \(\hat{R}\) are the unit vectors along \(\vec{A},\vec{B}\) and \(\vec{R}\), then the value of \(\vec{A}\cdot \vec{B}\) will be

If the resultant of \(\vec{A}=6\hat{A}\) and \(\vec{B}=8\hat{B}\) is \(\vec{R}=10\hat{R}\) where \(\hat{A},\hat{B}\) and \(\hat{R}\) are the unit vectors along \(\vec{A},\vec{B}\) and \(\vec{R}\), then the value of \(\vec{A}\cdot \vec{B}\) will be Correct Answer 0 

Correct option-3

Concept:

The parallelogram law:

Let R be the resultant of two vectors A and B.

According to the parallelogram law of vector addition, the resultant R is the diagonal of the parallelogram of which A and Bare the adjacent sides as shown in the figure.

Scalar or Dot Product

The scalar or dot product of two vectors A and B is denoted by A•B and is read as A dot B.

It is defined as the product of the magnitudes of the two vectors A and B and the cosine of their included angle θ.

Thus, A•B = AB cosθ (a scalar quantity)

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