Calculate projections of vectors

[ConeOfIce]

Homework Statement

Consider the following two vectors v1= (cosx , sinx)(transpose) , v2= (-sinx , cosx)(transpose). Compute the projectors P1, P2 onto the vectors v1 and v2.

Homework Equations

(a1) (a1*,b1*) (A) <---input
(b1) ...(B)
This is a matrix
that projects on
column
(a1)
(b1)

The snowman (one bracket over the other) is supposed to be a vector.

The Attempt at a Solution

I am completely lost on this situation. The textbook is extremely unclear, and there doesn't seem to be any information on line for how you go about projectors. Am I supposed to replace the input vector with v1, and then multiply it by the matrix to see what I get, or am I supposed to solve for a1 and b1, which I presume would be the projector. Any feedback would be great

Sorry if this comes out ugly.
Thanks.

 

[EnumaElish]

What are a1* and b1*? Is the projection you defined idempotent?