SOLUTION: If a = 2i - 2j - k and b = -4i + 3j - 2k a) find the angle between the vectors b) find the vector product.

Question 551151: If a = 2i - 2j - k and b = -4i + 3j - 2k
a) find the angle between the vectors
b) find the vector product.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
If a = 2i - 2j - k and b = -4i + 3j - 2k
a) find the angle between the vectors
b) find the vector product.
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a)
|a| = sqrt(2^2 + 2^2 + 1) = 3
|b| = sqrt(4^2 + 3^2 + 2^2) = sqrt(29)
Dot product = 2*-4 + -2*3 + -1*-2 = -12
a dot b = |a|*|b|*cos(angle)
-12 = 3sqrt(29)*cos(A)
cos(A) = -12/3sqrt(29)
A =~ 137.97 degs
----------------
b)
|+i +j +k|
|+2 -2 -1| = a X b
|-4 +3 -2|
= i*(4 + 3) - j*(-4 - 4) + k*(6 - 8)
= 7i + 8j + 2k

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