Vector and its components

  • #1

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


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


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.
 

Answers and Replies

  • #2
283
0
Note that
[tex]
F_{parallel} = |F|\cos{\theta}
[/tex]
(this is obvious if you draw two vectors on paper and apply a little trig)

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

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