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# zhou_1 - L MATH 103 TEST 1 3 IV(9 points Determine whether...

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MATH 103 TEST 1 NAME: Wednesday, Sept. 20, 2007 This test has six questions, worth a total of 70 points. Circle your answers. Show all your work. Unsupported answers may receive no credit. I. (9 points) Find the angle between the planes 2 x + 2 y - z = 15 and 7 y - z = 8. II. Let P 0 be the point (1 , - 1 , 2). Let L be the line x = 1+2 t, y = - 2+3 t, z = - t . a) (10 points) Find the distance from the point P 0 to the line L . b) (10 points) Find an equation for the plane which passes through the point P 0 and contains the line L . Typeset by A M S -T E X 1

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2 MATH 103 TEST 1 III. (20 points) The position vector r ( t ) = 2 cos ti + 2 sin tj + tk describes the motion of a particle on the helix. a) Find v , a , T and κ at the point (2 , 0 , 0). b) Find the length of this helix from the point (2 , 0 , 0) to the point (2 , 0 , 2 π ). c) Let L be the line tangent to this helix at the point (1 , 3 , 7 π 3 ). Find a parametric

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Unformatted text preview: L . MATH 103 TEST 1 3 IV. (9 points) Determine whether L 1 and L 2 intersect: L 1 : x = 2 t, y = 5-t, z = t ; L 2 : x = 1 + s, y = 2 + s, z = 3 + s. V. (6 points) Sketch the graphs of the following equations: a) z-y 2 + x 2 = 0 b) z 2-y 2-x 2 = 0 4 MATH 103 TEST 1 VI. (6 points) Determine if the following statements are True or False, and justify your answer brieﬂy. a) The points (2 , 1 ,-1), (3 , , 1) and (4 , 1 , 3) all lie on the same line. b) If the velocity of a particle moving in space is ~ V ( t ) = 1 t + 2 ~ i + ~ j + 2 t ~ k , and the initial position is (0 , , 0) at t = 0, then the particle’ position as a functin of t is ~ r ( t ) = ln | t + 2 | ~ i + t ~ j + t 2 ~ k ....
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