WIR_20B_M251-H1.pdf - Math 251 Summer 2020 Week-In-Review 1...

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Math 251 - Summer 2020 Week-In-Review 1 Math 251 - Week-In-Review 1 Justin Cantu Problem Statements You should attempt the problems yourself first. The next section contains the solutions. 1. What does y = 6 - z represent in R 3 ? 2. Find the center and radius of the sphere x 2 + y 2 + z 2 - x + 4 y - 10 z = 1 3. Find an equation of the sphere if one of its diameters has endpoints (2 , 1 , - 3) and (8 , 3 , 5). 4. Given the points A ( - 2 , 4 , 2) and B (3 , 0 , 8), find # » AB 5. Given a = h 1 , - 1 , 5 i and b = h- 3 , 2 , 1 i , find | a + 2 b | . 6. Find the vector that has the same direction as a = 2 i + j - 2 k but has length 5. 7. Compute a · b if (a) a = h 11 , - 2 , - 1 i and b = h 3 , 4 , - 7 i . (b) | a | = 5, | b | = 2, and θ = 30 . 8. Find the angle between the vectors a = h 4 , 2 , - 1 i and b = h- 3 , 0 , 4 i . 9. The points A (5 , 1 , 7), B (1 , - 2 , 3), and C (2 , - 1 , 6) form a triangle. Find ABC . 10. Find the scalar and vector projections of h 2 , 4 , 6 i onto h 1 , 3 , 5 i . 11. If a = h 3 , - 1 , 7 i and b = h 2 , 2 , 5 i , find b × a . 12. Find a nonzero vector that is orthogonal to the plane passing through the points P (0 , 1 , 2), Q (4 , - 2 , 5), and R (5 , 4 , - 3). .

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