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# pope1 - b onto a 7 Given the equation y=2x 2 – 4z 2 a...

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Math 22 Exam 1 Name: _________________ Fall 2000 (please print) 1. Given a = <-1, 5, 10> and ( a + b ) = <3,2,6>: a) Find 3 a b) Find | a + b | c) Find b . 2. Find <1,3,5> <3,-1,0> 3. Find <1,3,5> Χ < 1,2,3> 4a) Find parametric and symmetric equations for the line passing through (4,8,12) and (-2, 6, 3) b) Find a plane containing the origin perpendicular to the line in part a) 5. Are the points (0,0,0), (1,2,3), (5, 8, 9) and (3,12,3) coplanar? Why or why not? 6. Given the vectors a = i + j + k and b = 2 i + 6 j + 4 k , find the vector projection of
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Unformatted text preview: b onto a . 7. Given the equation y=2x 2 – 4z 2 a) Name the surface this equation describes. b) Sketch the trace of the surface in the planes: y=0, y=1 and y=-1 8. Describe the graph of θ =0 in spherical coordinates. 9. A particle moves with position function: r(t)=<t 2 , t 2 , t 3 > Find: a) the tangential component of acceleration b) the normal component of acceleration c) the curvature at time t d) the unit tangent vector at time t e) At the time t=1, how far is the particle from the plane x+y+z=1...
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