Why use cos for dot product and sin for cross product?

[Mamoon]

Dose anybody knw that why we take cos with dot product and Sin with cross product?

 

[jedishrfu]

Welcome to PF!

They are complementary operations.Tthe dot product gives you the part of vector A projected onto B whereas the cross product gives you the part of A not projected onto B and vice versa.

A dot B = |A| |B| cos(AB) and the project of A on B = |A| cos (AB) = (A dot B) / |B|

The cross product also gives you a vector normal to both A and B using the righthand rule by convention.

There are other geometric ways of looking at it too. The cross product is the area of the parallelogram with A and B as its sides.

 

[HallsofIvy]

The dot product is related to the projection of one vector on another. If you draw vectors u and v with "ends" together and drop a perpendicular from the tip of vector u to vector v, then you have a right triangle in which the length of u is the hypotenuse and the length of the projection is the "near side".