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ww4 - Jignesh Patel due at 11:59pm EDT Assignment 4 MATH262...

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Jignesh Patel Assignment 4 MATH262, Fall 2010 due 10/13/2010 at 11:59pm EDT. 1. (1 pt) Let a = (7, 6, 6) and b = (5, 5, 1) be vectors. Compute the cross product a × b . ( , , ) 2. (16 pts) Consider the 3 points P = ( 5 , - 7 , 7 ) , Q = ( - 2 , 8 , - 8 ) and R = ( 4 , - 5 , - 4 ) . 1. The equation of the plane passing through P,Q,R is x + y + z + = 0 2. The parametric equations of the line L through P,Q are x = + t y = + t z = + t 3. The equation of the plane perpendicular to L and passing through R is x + y + z + = 0 3. (1 pt) This question has two parts. 1. The point on the line x = 2 - 3 t , y = - 1 - t , z = - 2 + 3 t which is closest to the point (-1,2,2) is ( , , ). 2. The point on the plane - 3 x + 3 y - 3 z = 2 that is closest to the point (2,-1,-3) is ( , , ). 4. (1 pt) Find points P,Q which are closest possible with P lying on the line x = - 1 + 2 t , y = - 1 - 2 t , z = 3 - 6 t and Q lying on the line x = - 21 + 2 t , y = 27 , z = 7 - 2 t . P = ( , , ) Q = ( , , ) 5. (1 pt) If r ( t ) = cos ( 4 t ) i + sin ( 4 t ) j - 6 t k , compute: A. The velocity vector v ( t ) = i + j + k B. The acceleration vector a ( t ) = i + j + k Note: the coefficients in your answers must be entered in the form of expressions in the variable t; e.g. “5 cos(2t)” 6.
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