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What is the answer if vector A is multiplied with vector B?

In vector multiplication, there are two types of multiplication: One in which the result is a scalar and the other in which the result is a vector.

Accordingly the two types of products of vectors are:

Scalar product (also called dot product) denoted byA.B

Vector product (also called cross product) denoted by AxB

A.B  = AB cos Θ, where Θ is the angle between the directions of A and B

The physical meaning of dot product is that, “The product of the magnitude of one vector and the magnitude of the component of the other vector in the direction of the first vector.”

AxB = AB sinΘ \hat{n}

The direction of cross product is given by right hand cork screw rule

cross product

Difference between Scalar Product and Vector Product

“What is the difference between dot product and cross product?” [The question was posted by Salman)

Examples of scalar product and vector product

Kashan asks:

“will you give me min 10 examples 0f scalar product and vector product known at xii level”

I am just strating the list; members please contribute more as comments

Scalar Product

  1. work F.s
  2. Power F.v
  3. Potential energy of a dipole P.E

 

Vector Product

  1. Torque on a dipole = PxE
  2. Lorentz magnetic force F=qvxB
  3. Torque =rxF

 

 

Difference between dot product and cross product

Shashi Kant asked:

“What is difference between cross product and dot product?”

 

Answer:

If the product of two vectors is a scalar quantity it is called scalar product or dot product.

If the product of two vectors is a vector quantity it is called vector product or cross product.

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