Hw12-3

# Hw12-3 - Math 1920 Solutions Section 12.3 12.3.8 Find the...

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Section 12.3 12.3.8 Find the following: (a) ~v · ~u , | ~v | , | ~u | (b) Cosine of angle between ~v and ~u (c) Scalar component of ~u in the direction of ~v (d) Vector proj ~v ~u We have: ~v = ± 1 2 , 1 3 ² ~u = ± 1 2 , - 1 3 ² ~v · ~u = 1 6 | ~v | = 30 6 | ~u | = 306 cos θ = 1 5 | ~u | cos θ = 1 30 proj ~v ~u = 1 5 ³ 1 2 , 1 3 ´ 12.3.12 Find the angles between the vectors ~u = i + 2 j - 2 and ~v = - i + j + k to the nearest hundredth of a radian. Use deﬁnition of θ . θ = cos - 1 µ ~u · ~v | ~u || ~v | = cos - 1 (1)( - 1) + ( 2)(1) + ( - 2)(1) q (1) 2 + ( 2) 2 + ( - 2) 2 p ( - 1) 2 + (1) 2 + (1) 2 = cos - 1 µ - 1 5 3 = cos - 1 µ - 1 15 1 . 83 rad 12.3.15 Using the deﬁnitions of direction angles and direction cosines, show (a) cos α = a | ~v | , cos β = b | ~v | , cos γ = c | ~v | , and cos 2 α + cos 2 β + cos 2 γ = 1 (b) If ~v = a ~ i + b ~ j + c ~ k is a unit vector, then a, b, and c are the direction cosines of

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## This note was uploaded on 06/11/2011 for the course MATH 1920 at Cornell.

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Hw12-3 - Math 1920 Solutions Section 12.3 12.3.8 Find the...

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