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## Homework Statement

Consider the two vectors:

L = 4 i + 3 j + k

and

s = 6 i + 6 j + 8 k

Find the value of the scalar α such that the vector

L - αs

is perpendicular to L.

## Homework Equations

Dot Product:

A [tex]\bullet[/tex] B = |A||B| cos(theta)

A [tex]\bullet[/tex] B = A

_{x}B

_{x}i + A

_{y}B

_{y}j + A

_{z}B

_{z}k

A [tex]\bullet[/tex] A = (Ax^2 + Ay ^2 + Az^2)^.5 (Wouldn't let me do sub and sup in sqrt)

Cross Product

A x B = |A||B| sin(theta)

## The Attempt at a Solution

I thought that I could do AxB and set that equal to |A||B| cos(theta) but when I did that everything just canceled out. I am really confused about multiplying a vector by a scalar and how that changes orientation etc.

Any help appreciated!

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