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# math22 - EXAM 1 MATH 22 Winter 2001 Name Section You have...

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EXAM 1 MATH 22 Name: ____________________________ Winter 2001 Section: __________ You have 50 minutes to complete this test. You must show all work to receive full credit. 1. Given , and . Find the following: a = < - 11 2 , , b = < - 01 1 , , c = < - 11 0 , , (a) , (b) The angle between and . a b + a b (c) A unit vector that is orthogonal to both and . b c 2. Determine whether the lines and are parallel, skew or intersecting. If they intersect find the point of L 1 L 2 intersection. : , , , : , , . L 1 x t = - 6 y t = + 1 9 z t = - 3 L 2 x s = + 1 2 y s = - 4 3 z s = 3. Given the points , , and . P ( , , ) 01 2 Q ( , , ) 2 4 5 R ( , , ) - 1 01 S ( , , ) 6 14 - (a) Find the volume of the parallelepiped determined by the vectors , and . PQ PR PS (b) Are the three vectors , and coplanar? Explain. PQ PR PS 4. (a) Find an equation of the plane through the point and perpendicular to the line , ( , , ) - 2 8 10 x t = + 1 , . y t = 2 z t = - 4 3 (b) Find the distance from the point to the plane . ( , , ) 0 10 - x y z - - = 2 2 1 5. Find the traces of the surface given by in the planes

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math22 - EXAM 1 MATH 22 Winter 2001 Name Section You have...

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