# B find the volume of the box generated by the vectors

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(b) Find the volume of the box generated by the vectors a = i + j - k , b = i - j + k and c = - i + j + k .

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CALCULUS II, TEST I 5 Problem 3 Consider the two lines given by the parametric equations 1 = x = 2 t y = - 2 + 2 t z = 4 - t and 2 = x = 10 s y = 3 + 5 s z = - 3 + 2 s (a) Determine whether they are parallel. (b) Determine whether they intersect. If they do intersect, find the point of intersection. (c) Determine whether they are skew.
CALCULUS II, TEST I 6 Problem 4 This problem has two separate questions (a) and (b). Answer each question. (a) Find the parametric equations of the line of intersection of the planes x + 2 y + 2 z = 1 and x - 2 y + 3 z = 1 . (b) Find the distance from the point P (3 , 2 , 1) to the plane x = 0.

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CALCULUS II, TEST I 7 Problem 5 A particle is traveling along the space-curve r ( t ) = h 4 cos( t ) , 2 sin( t ) , t i when t 0. (a) Determine the velocity vector of the particle at the time t = π . (b) Find the parametric equations of the tangent line to this space-curve when t = π .
CALCULUS II, TEST I 8 SCRATCH PAPER

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CALCULUS II, TEST I 9 SCRATCH PAPER
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