Multiplication of a vector by another vector does not follow the laws of ordinary algebra. There are two types of vector multiplication
(i) Scalar product and (ii) Vector product.

*Multiplication of two vectors*

Multiplication of a vector by another vector does not follow the laws of ordinary algebra. There are two types of vector multiplication

(i) Scalar product and (ii) Vector product.

*(i) Scalar product or Dot product of two vectors*

If the product of two vectors is a scalar, then it is called scalar product. If Vector A and Vector B are two vectors, then their scalar product is written as Vector A.

Vector B and read as Vector A dot Vector B. Hence scalar product is also called dot product. This is also referred as inner or direct product.

The scalar product of two vectors is a scalar, which is equal to the product of magnitudes of the two vectors and the cosine of the angle between them. The scalar product of two vectors Vector A and Vector B may be expressed as Vector A . Vector B = | Vector A| | Vector B| cos θ where | Vector A| and | Vector B| are the magnitudes of Vector A and Vector B respectively and θ is the angle between Vector A and Vector B as shown in Fig.

*(ii)*** Vector product or Cross product of two vectors**

The vector product or cross product of two vectors is a vector whose magnitude is equal to the product of their magnitudes and the sine of the smaller angle between them and the direction is perpendicular to a plane containing the two vectors.

If θ is the smaller angle through which Vector A should be rotated to reach Vector B, then the cross product of Vector A and Vector B (Fig.) is expressed as,

Vector A x Vector B = | Vector A| | Vector B| sin θ ^n = Vector C

where | Vector A| and | Vector B| are the magnitudes of Vector A and Vector

B respectively. Vector C is perpendicular to the plane containing Vector A and Vector B. The direction of Vector C is along the direction in which the tip of a screw moves when it is rotated from Vector A to Vector B. Hence Vector C acts along OC. By the same argument, Vector B ? Vector A acts along OD.

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