MA 261 EXAM 1 Form A Sprin g 2008Answer Key: DCAC DADB ECBB1. Find all values of x so that the vectors a = (x, −3, 1), b = (x, x, 2)are perpendicular. The correct values of x areA. 0, 1B. −1, 2C. 1, 1D. 1, 2E. 2, 22. Determine a so that the linex − 37=y + 5a=z + 14is para llel to the plane 2x + 3y − 5z = 1 0 . Th e correct choice ofa isA. 1B. 3C. 2D. −2E. −13. Determine a so that the lines x = a + t, y = −3 + 2t, z = t andx = 1 + s, y = 2 − s, z = 2s intersect. The correct choice of a isA. 0B. 1C. −1D. 2E. −21MA 261 EXAM 1 Form A Sprin g 20084. The equation of the plane perpendicular to the linex − 1−2=y − 13= zand containing the point (1, 1, 1) isA. x + y − z = 1B. 2x − 3y + z = 0C. −2x + 3y + z = 2D. 2x + 3y − z = 4E. 3x − 2y + z = 25. The surface whose equation in spherical coordinates isφ = π representsA. a planeB. a cone with axis the z-axisC. the xy planeD. the negative z axisE. the z axis6. Let L be the line tangent to the curve r(t) = (ln t, 2√t, t2) at(0, 2, 1). Then when L passes through the point (3, y, z), we haveA. y = 5 and z = 7B. y = 3 and z = 3C. y = 7 an d z = 5D. y = 3 and z = 6E. y = 4 and z = 52MA 261 EXAM 1 Form A Sprin g 20087. The curve r(t) = (e2t, −et), − ∞ < t < ∞, has a graph most like8. Let a particle move on the curve r(t) = 5ti + (1 − 3t)j + (5 +4t)k, starting when t = 0. After it has gone a distance 2, the xcoo rdinate isA. 10B.√2C. 5√2D. 1/10E. 5/√23MA 261 EXAM 1 Form A Sprin g 20089. Let u = e2xsin(xy). Then uxy= A. e2x(x + 1) cos(xy) − xy sin(xy)B. e2x(x + 1) cos(xy) + xy sin(xy)C. e2x−(x+ 1) cos(xy)−xy sin(xy)D. e2x(2x + 1) cos(xy) + xy sin(xy)E. e2x(2x + 1) cos(xy) − xy sin(xy)10. Let Π be the tangent plane to the paraboloi d z = x2+ 2 y2+ 6 atthe po int (1, 1, 9). Then Π intersects the z-axis whenA. z = 1B. z = 2C. z = 3D. z = 4E. z = 54MA 261 EXAM 1 Form A Sprin g 200811. The level curve f(x, y) = 2 o f the functionf(x, y) = x2− y2+ 8x − 7 isA. a parabolaB. a hyperbolaC. two linesD. an ellipse but not a circleE. a circle12. The trajectory of a moving particle is given byr(t) =t2/2 − t, cos(t − 1), ln(1 + t) − t/2.When the speed is zero, the acceleration a isA. (0, 0, 0)B. (1, −1, −14)C. (1, −1,14)D. (1, 1, −14)E. (1,
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