m1b-20C-fa2005

# m1b-20C-fa2005 - 2 x y-z =-1(a Does the line intersect the...

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Print Name: Student Number: Math 20C. Midterm Exam 1 October 17, 2005 Read each question carefully, and answer each question completely. Show all of your work. No credit will be given for unsupported answers. Write your solutions clearly and legibly. No credit will be given for illegible solutions. 1. (6 points) Consider the vectors v = h 6 , 2 , - 3 i and w = h- 2 , 2 , 1 i . (a) Find a vector normal to both, v and w . (b) Find the area of the parallelogram formed by v and w . (c) Find a vector of length one in the direction of w . # Score 1 2 3 4 Σ

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2. (6 points) Find an equation for the plane that passes through the points ( - 1 , 1 , 1), ( - 1 , - 1 , 1), and (0 , 0 , 2).
3. (6 points) Consider the line given by r ( t ) = h 0 , 1 , 1 i + h 1 , 2 , 3 i t and the plane given by

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Unformatted text preview: 2 x + y-z =-1. (a) Does the line intersect the plane? If yes, Fnd the intersection point. In any case, justify your answer. (b) ±ind the equation of the line, passing through the point (0 ,-1 ,-1) and orthogonal to the plane given above. 4. (6 points) A particle moves in a plane with a velocity function given by the expression v ( t ) = h 3 sin( t ) , 2 cos( t ) i , for t ≥ 0. (a) Find the acceleration a ( t ) function of the particle. (b) Find the position function r ( t ) of the particle knowing that the initial position of the particle is r (0) = h-1 , 1 i ....
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m1b-20C-fa2005 - 2 x y-z =-1(a Does the line intersect the...

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