exam1 - ( 15 pts ) (b) An equation for the plane determined...

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Exam #1 Mat 214 Sec ____ Name: _____________ Oct 20, 2008 Pts : _________/150 Show all work on the pages of this exam. You may use a scientific calculator only . 1. The angle between the vectors a and b is 120°, a = 5, and b = 8. (a) Determine the dot product a b and (b) the magnitude of the cross product a x b. ( 10 pts ) 2. Two points A and B have the given coordinates A = (5,-3,2) and B = (-1,-4,3). Find the unit vector in the direction of the directed line segment AB . ( 15 pts ) 3. Given the vectors a = < 4, -3, 1 > and b = < -1, -2, 2 > find a decomposition of a into the sum of a vector parallel to b and a vector perpendicular to b . ( 15 pts )
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3. Given the points P = (2, -1, 1), Q = (-3, 2, 0), and R = (4, -5, 3) (a) Find parametric equations of a line through the point Q and parallel to the line through the points P and R.
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Unformatted text preview: ( 15 pts ) (b) An equation for the plane determined by P, Q, and R. ( 15 pts ) (c) The area of the triangle PQR. ( 15 pts ) 4. Show that the two lines intersect. Find the point of intersection and the angle between the lines. ( 15 pts ) L 1 : r (t) = ! 2 + t, 1 + t, 4 + 7t ! L 2 : r (s) = !-4 + 5s, 2-2s, 1-4s ! 5. Identify and sketch the surfaces given below. ( 15 pts ) (a) y 2- 4 = z (b) 2x + 3y + 4z = 12 6. Identify the traces of the given surface in the planes x = k, y = k, and z = k. Then identify the surface and sketch it .( 20 pts ) x 2 4 + z 2 = 9 y 7. The equation z = x 2 + y 2 represents the upper half of a cone which can be written as z 0, z 2 = x 2 + y 2 . Find the spherical coordinate equation of this cone. ( 15 pts )...
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exam1 - ( 15 pts ) (b) An equation for the plane determined...

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