SecBEx1W01 - ( , , ) 11 2 (4pts) (b) Write in cylindrical...

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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 clearly to receive full credit. (10pts) 1. Find an equation of the sphere passing through the origin and whose center is . ( , , ) 3 2 3 (6pts) 2. For what values of are the vectors and orthogonal? c < - 6 2 , , c < c c c , , 2 (6pts) 3. Find the direction cosines of . a =< 3 2 3 , , (8pts) 4. Find the distance between the planes and . 3 4 2 x y z + - = 3 4 24 x y z + - = (10pts) 5. Determine whether the planes are parallel, perpendicular or neither. If neither, find the angle between them. and x y + = p y z + = p (6pts) 6. Find the parametric equations of the line passing through and perpendicular to ( , , ) 12 3 the plane . 3 2 10 x y z + - = 7. (6pts) (a) Change the point from rectangular to spherical coordinates.
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Unformatted text preview: ( , , ) 11 2 (4pts) (b) Write in cylindrical coordinates. x y z y 2 2 2 2 + + = 8. Given . Find the following: r t t i j t k = + -( ) cos( ) sin( ) 2 2 (6pts) (a) unit tangent vector T t ( ) (6pts) (b) unit normal vector N t ( ) (6pts) (c)curvature at k ( , , ) 110 (2pts) (c) N t x N t &quot; &quot; ( ) ( ) (6pts) (d) Find the arc length of the curve from to . r t ( ) t = t = p 2 9. A moving particle starts at an initial position with initial velocity . r j = ( ) V i k = + ( ) Its acceleration is . Find the following: a t j = ( ) (6pts) (a) the speed V at t = 2 (6pts) (b) the position vector r t ( ) (6pts) (c) the tangential component of acceleration at . a T t = 1...
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