**Unformatted text preview: **~v , ~u × ~v , the angle between ~u and ~v , and the vector of length 1 that points in the same direction as ~v . Solution: ~u · ~v = 2 · 0 + (-1) · 2 + 3 · 3 = 7 ~u × ~v = µ µ µ µ µ µ ~ ı ~ ~κ 2-1 3 2 3 µ µ µ µ µ µ = h-9 ,-6 , 4 i To ﬁnd the angle between ~u and ~v , use the formula ~u · ~v = | ~u | · | ~v | · cos θ : θ = cos-1 ± ~u · ~v √ ~u · ~u · √ ~v · ~v ² = cos-1 ± 7 √ 14 · √ 13 ² = cos-1 (0 . 5188745215) , which is 1 . 025262482 radians or 58 . 74321311 ◦ . The vector of length 1 that points in the same direction as ~v is ~v | ~v | = h , 2 , 3 i √ 2 + 2 2 + 3 2 = ³ , 2 √ 13 , 3 √ 13 ´ ....

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- Spring '08
- Brewer
- Calculus, Trigonometry, Elementary geometry, θ, 1.025262482 radians