Question

why cross and dot product is used?

Answer 1

Cross product between two vectors is used to describe the area vector formed by the two vectors.

Suppose, A and B be two vectors, let θ be the angle between the two vectors

Area of parallelogram formed by the two vectors will be:

C = ABsinθ

Direction of the area so formed is normal to the plane of the parallelogram.

C = ABsinθ n

nis the unit vector in the direction of normal to the area.

Dot product is used to find the product of magnitude of one vector and magnitude of projection of another vector on it.

Let F and S be two vectors, let θ be the angle between the two vectors

Projection of S on F will be Scosθ.

So, now product of F and Scosθ gives the dot product of the two vectors.

W = FScosθ.