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There are two ways in which a vector can be  multiplied by another vector:

(i) One way produced a scalar and is known as scalar product.

(ii) Another way produces a new vector and is known as vector product.

Scalar or dot product.

The scalar or dot product of two vectors is defined as the product of the magnitudes of and cosine of the angle between them. Thus

As A, B and cos are all scalars,  so the dot product of  is a scalar quantity. Both have directions, but their dot product has no direction.

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