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MAC2313_Test1_Spring2010

# MAC2313_Test1_Spring2010 - the sphere x 2 y 2 z 2 = 5 6(8...

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Page 1 of 4 MAC 2313 Name_________________________________ Test 1 Date: January 21, 2010 Clearly show all work for full credit. 1. (6 points) Find an equation of a sphere if one of its diameters has endpoints (2,1,4) and (4,3,10). 2. (6 points each) Given points P(1,-3,-2), Q(6,-2,-5), and R(2,0,-4) in R 3 , (a) determine whether PQR Δ is a right triangle. (b) determine the area of PQR Δ .

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Page 2 of 4 3. (3 points each) Given k j a 4 3 = and k j i b + = 2 2 , compute each of the following: (a) 3 b – 2 a (b) | a | (c) b a (d) b a × (e) the angle θ between a and b (f) a unit vector in the direction of b 4. (8 points) Suppose the trajectories of two particles are given by the vector functions r 1 ( t ) = < t , t 2 , t 3 > and r 2 ( t ) = < 1+2 t , 1+6 t , 1+14 t > for t > 0. Determine whether the particles collide and, if so, the point at which the collision occurs.
Page 3 of 4 5. (8 points) Determine the point(s) at which the curve r ( t ) = < sin( t ), cos( t ), t > intersects

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Unformatted text preview: the sphere x 2 + y 2 + z 2 = 5. 6. (8 points) Determine symmetric equations for the line in R 3 through the points P(6,1,-3) and Q(2,4,5). 7. (8 points) Find an equation of the plane through the point (-1,6,-5) and parallel to the plane x + y + z + 2 = 0. 8. (8 points) Find parametric equations of the line of intersection of the planes 3 x – 2 y + z = 1 and 2 x + y – 3 z = 3. Page 4 of 4 9. (8 points) Determine whether the lines L 1 and L 2 given below are parallel, skew, or intersecting. If they are intersecting, find the point of intersection. L 1 : 3 2 2 1 2 − = − = + z y x L 2 : 2 1 3 2 4 3 − = − − = − − z y x 10. (8 points) Find an equation of the plane that passes through the point (1,2,3) and contains the line x = 3 t , y = 1 + t , z = 2 – t . 11. (8 points) Find the distance from the point (-6,3,5) to the plane x – 2 y – 4 z = 10....
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MAC2313_Test1_Spring2010 - the sphere x 2 y 2 z 2 = 5 6(8...

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