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iclutcha
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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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