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## Homework Statement

The cosine of the angle between vector a and vector b is 4/21. Find p.

vector a = 6i + 3j - 2k

vector b = -2i + pj - 4k

## Homework Equations

(Vector a) . (Vector b) = abcos(theta)

(Vector a) . (Vector b) = axbx + ayby + azbz

mag(a) = root(ax^2 + ay^2 + az^2)

## The Attempt at a Solution

mag(a) = root(36 + 9 + 4) = 7

mag(b) = root(4 + p^2 + 16) = root(p^2 + 20)

(Vector a) . (Vector b) = -12 + 3p + 8 = 3p - 4

(Vector a) . (Vector b) = abcos(theta)

3p - 4 = 7[root(p^2 + 20)](4/21)

3p - 4 = [4/3][root(p^2 + 20)]

Square both sides

9p^2 - 24p + 16 = 16/9p^2 + 320/p

Collect like terms, and set equation to 0

(65/9)p^2 - 24p - 176/9

Sub into quadratic equation

p = 4

p = -44/65

[CORRECT ANSWER: P = 4]

Thanks for the help ;)

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