How to Resolve a Vector into Parallel Components?

[blackandyello]

Homework Statement

Resolve the position vector A of the car (measured from fixed point O)
into components parallel to OB and OC.

Figure: http://screensnapr.com/e/4D2OAz.png

Homework Equations

Projection of vector A to OC = |A| * |unit vector OC| * unit vector

The Attempt at a Solution

my solution for finding the component parallel to OC is by finding the angle of triangle AOC, then use that angle to compute for parallel component at OC. my answer ended up to be the same 3500m. but the book says, 2570m along OC.

 

[humanist rho]

A.B = ABCosθ is the projection of vector A along B.

 

[JHamm]

A.B = ABCosθ is the projection of vector A along B.

But if you take $B = A$ then you find the projection of $A$ along $A$ is $A^2$

 

[humanist rho]

But if you take $B = A$ then you find the projection of $A$ along $A$ is $A^2$

oh sorry. I mean B cosθ is the projection of B along A.