Question

how do we find the projection of one vector on to another vector?

Answer 1

Hey.

The vector projection of a vector a on (or onto) a nonzero vector b (also known as the vector component or vector resolution of a in the direction of b) is the orthogonal projectionof a onto a straight line parallel to b. It is a vector parallel to b, defined as

vector a = |a| unit vector b

where |a| is a scalar, called the scalar projection of a onto b, and b̂ is the unit vector in the direction of b. In turn, the scalar projection is defined as

A1= |a|cos θ = a • b̂ =a. b/|b|

where the operator · denotes a dot product, |a| is the length of a, and θ is the angle between a and b. The scalar projection is equal to the length of the vector projection, with a minus sign if the direction of the projection is opposite to the direction of b.

Thanks.