How Do You Calculate the Parallel and Perpendicular Components of a Vector?

[hadroneater]

Homework Statement

force vector F = 700[-0.25, 0.433, 0.866].
vector A = [-4, 4, 2]
a)What is the component of F that is parallel to A?
b}And what is component of F that is perpendicular to A?

Homework Equations

A\bullet F = |A||F|\cos{\theta}
When two vectors are parallel:
A\bullet B = |A||B||
When two vectors are perpendicular
A\bullet B = 0

The Attempt at a Solution

I'm not sure if I should use the dot product to find the component but I figure that would be the simplest way to do so.
A = [-4, 4 ,2] = 6[-2/3, 2/3, 1/3]
The parallel force vector = s[-2/3, 2/3, 1/3]
That's all I have right now. If I use the dot product equation, both sides of the equation will come to the same term and cancel each other out. I think my definition for the parallel force vector is too general as s could be any scalar.

 

[JaWiB]

Note that
<br /> F_{parallel} = |F|\cos{\theta}<br />
(this is obvious if you draw two vectors on paper and apply a little trig)

So
<br /> A\bullet F = |A|F_{parallel}<br />
Then just use the definition of the dot product to calculate the left hand side and solve for the parallel component