my book asks me to find the vector projection of u onto v. Then it says to write uas a sum of two orthogonal vectors, one of which is proj(subscript v)u.

then it gives me the vectors u= and v=

I don't understand how to solve this problem, can anyone help me understand?:confused:

sorry the vector part should read
u = (3, -7) and v = (-2, -6)

To project one vector on another, usually you take the magnitude of the first vector and multiply it by the cosine or sine of the angle between them, depending on the orientation of the vector.

Usually, you take a vector and obtain the horizontal and vertical components of the vector by placing the vector in a cartesian coordinate system. The Y-component is orthogonal to the X-component. This sounds like what this is trying to do.

Does this make sense to you?