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Expert: Sherry Wallin - 11/8/2009
Question
I need help with this problem, please:
Suppose points A, B, and C have coordinates A (0, 0), B (1, –2), and C (4, 2).
Let u be the vector with initial point A and terminal point B.
Let v be the vector with initial point B and terminal point C.
Find the angle between u and v. Round the result to the nearest tenth of a degree.
Thank you!
Answer
u= (1-0,-2-0) = (1,-2)
v= (4-1,2--2) = (3,4)
cos x = u dot v/|u||v| = 1(3) -2(4)/sqrt(1^2+(-2)^2)*sqrt(3^2+4^2) = [3-8]/sqrt(5)*sqrt(25)
= -5/[5sqrt5] = -1/sqrt5
that is that cos x = -1/sqrt5 but you want x (the angle between u and v) so you need to take the
cos^-1(-1/sqrt5) ~= 116.6 degrees
Math Prof
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