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Physics XI Notes for Physics Notes

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Multiplication Of Two Vectors

There are two types of the multiplication of two vectors:

  • Scalar product OR dot product
  • Vector product OR cross product

Scalar product
OR
Dot product

Type of multiplication of two vectors in which the product is a scalar quantity is referred to as “scalar product OR dot product”

Mathematical representation of scalar product

Consider two vectors and making an angle q with each other. Their scalar product or dot product is defined as:
Scalar product of two vectors and is a scalar quantity which is equal to the
product of the magnitudes of and the cosine of the angle between them.

Explanation
Example 1:
When we multiply two vector quantities force and displacement we get work which is a scalar quantity. Therefore, we can say that work is the scalar product or dot product of force and displacement.

Example 2:
When we multiply two vector quantities electric intensity and normal area we get electric flux which is a scalar quantity. Therefore, we can say that electric flux is the scalar product or dot product of electric intensity and normal area

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