Solutions5 - MATH 214 A1 - Assignment 5 Due Friday, June...

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Unformatted text preview: MATH 214 A1 - Assignment 5 Due Friday, June 10, 5:00pm (1) (a) Find the equation of the plane containing the points (0 , , 2), (1 , , 0) and (1 ,- 1 , 1). (2 marks) 2 x + y + 2 (b) Find the distance between the plane calculated in part ( a ) and the point (3 , , 10). (3 marks) Let P = (0 , , 2) and P = (3 , , 10), then d = P P n | n | = h 3 , , 8 i h 2 , 1 , 1 i |h 2 , 1 , 1 i = 14 6 (2) Given the vector-valued function r ( t ) = h 4 9 (1+ t ) 3 2 , 4 9 (1- t ) 3 2 , 1 3 t i : (a) Find r ( t ) (2 marks) r ( t ) = h 2 3 1 + t,- 2 3 1- t, 1 3 i (b) Find a ( t ) (2 marks) a ( t ) = h 1 3 1 + t , 1 3 1- t , i (c) Find the angle between the two vectors. (3 marks) cos( ) = r a | r || a | = | r || a | = 0 Thus the two vectors are perpendicular. (3) If an object starts at rest with initial position vector h , , i at t = 1 and undergoes acceleration described by a ( t ) = h 1 t , 1 5- t , 1 2 t i from t = 1 to t = 3: (a) Find the velocity at time t = 2 (2 marks) The velocity...
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Solutions5 - MATH 214 A1 - Assignment 5 Due Friday, June...

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