# Vector and its components

1. Jan 21, 2010

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
$$A\bullet F = |A||F|\cos{\theta}$$
When two vectors are parallel:
$$A\bullet B = |A||B||$$
When two vectors are perpendicular
$$A\bullet B = 0$$

3. 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.

2. Jan 22, 2010

### JaWiB

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

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