orick1 - paraboloid x 2 + 2y 2 z =0 in terms of both...

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MATH 22 Exam 1 Name: ______________________ FALL, 2000 1. (5 pts.) Write an inequality to describe the region inside the sphere of radius 2 centered at the point (2, 0, 0). 2. (10 pts.) Given the vectors a = <1, 2, 3>, and b = <-1, 1, 4> calculate: (a) 3 a – 2 b (b) | a | (c) the angle between the vectors a and b 3. (12 pts.) Find the volume of the parallelepiped determined by the three vectors PQ , PR , and PS with the points P(0, 1, 2), Q(3, 1, 2), R(4, 1, 3), and S(2, 1, 3). Are the three vectors PQ , PR , and PS co-planar? YES NO (circle one) 4. (10 pts.) Find the symmetric and parametric equations of the line containing the point P(2, 4, 0) and perpendicular to the plane 3x + y –2z = 10. 5. (12 pts.) Find the traces of the surface given by x 2 – 4y 2 +9z 2 = 1 in the planes y = k (for several values of k) and identify the surface. 6. (9 pts.) Express the rectangular coordinates and the equation for the elliptic
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Unformatted text preview: paraboloid x 2 + 2y 2 z =0 in terms of both cylindrical and spherical coordinates. 7. (10 pts.) A particles velocity is given by v (t) = cos( t ) i t k . At time t = 0, the particles passes through the point (1, 1, 2). Find an equation for the particles position r (t). 8. (16 pts.) Given r (t) = cos(2 t ) i + t j sin(2 t ) k find the following: (a) unit tangent vector T (b) unit normal vector N (d) curvature at the point (-1, p/2, 0) 9. (16 pts.) A particle follows a path determined by the vector function r (t) = cos( t ) i + e t j 4 t k find: (a) particle velocity (b) particle speed (c) tangential and normal components of the acceleration at time t = 0. (d) write an integral expression for the length of the path traversed by the particle between the points (1, 1, 0) and (0, e p/2 , -2p). It is not necessary to evaluate the integral....
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This note was uploaded on 01/24/2011 for the course MATH 22 taught by Professor Brigham during the Winter '08 term at Missouri S&T.

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