WA 10 Vectors DotandCross Products.pdf - Name Math 172 Spring 2019 Written Assignment 10 Vectors Dot Product Cross Product 1 Define the points(\u22123

# WA 10 Vectors DotandCross Products.pdf - Name Math 172...

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Name ________________________ Math 172 Spring 2019 Written Assignment 10: Vectors, Dot Product, Cross Product 1. Define the points ?(−3, −1), ?(−1, 2), ?(1, 2), ?(3, 5), ?(4, 2) and ?(6, 4) . (a) Sketch ?? ⃗⃗⃗⃗⃗ , ??, ⃗⃗⃗⃗⃗⃗ and ?? ⃗⃗⃗⃗⃗ and the corresponding position vectors. (b) Find the equal vectors among ?? ⃗⃗⃗⃗⃗ , ?? ⃗⃗⃗⃗⃗ and ?? ⃗⃗⃗⃗⃗ 2. Given ? = ⟨4, −3, 0⟩ and ? = ⟨1, 2, 3⟩ , (a) Find 3? + 2? (b) Find |3? + 2?| (c) Find the unit vector in the direction of 3? + 2? .
Name ________________________ 3. Compute the dot product of the vectors ? and ? , and find the angle between the vectors: ? = −3? + 4?, ? = −4? + ? + 5? . 4. Find the scalar component of ? in the direction of ? , scal v ? and the orthogonal projection of ? onto ? , proj v ? , for the vectors ? = −3? + 4?, ? = −4? + ? + 5? .
Name ________________________ 5. Compute the cross product ⟨4, 1, −2⟩ × ⟨1, 1, 0⟩ . 6. Find the area of the triangle whose vertices are the points ?(1, 0, 3), ?(5, 0, −1) and ?(0, 2, −2) .