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## Homework Statement

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Here are two displacements, each measured in meters:

A. 4i+5j-6k

B. -1i+2j+3k

What is the component of A that is perpendicular to the direction of B and in the plane of A and B.?

## Homework Equations

The book gave me a hint to use this equation:

http://puu.sh/fFya9/3d102e2d2f.png [Broken]

c being the magnitude of the result of A cross B. a and b being the magnitudes of vectors A and B.

## The Attempt at a Solution

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I plugged the values into that:

c=(8.775)*(3.742)*sin(111.438)

c=30.564

I don't see how that is supposed to help me.

A cross B gives me the vector:

C=27i-6j+13k

This vector is perpendicular to the A,B plane.

Would I need to cross C by B again to get it back in the A,B plane? After doing that would I need to use this equation to find the final component part?

Doing that gives me:

D=-44i-94j+48k

A dot D=-934

-934=8.775*114.35*cos(phi)

phi=158.56

I think this is the angle between vectors A and D. Then is it just a*cos(158.56)

8.77*cos(158.56)=-8.17

I'm not 100% sure that is correct as I feel I messed up with being able to cross product twice to get back on the A,B plane. Your help is greatly appreciated.

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