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# self quiz 3 answers - MATH 210 Self-quiz 3 1 Consider the...

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MATH 210 Self-quiz 3 February 01, 2009 1. Consider the motion given by the vector valued function r ( t ) = < 3 sin(2 t ) , 3 cos(2 t ) , t > . Find its velocity, its acceleration and its speed. Solution: The velocity is given by: v ( t ) = r ( t ) = < 6 cos(2 t ) , - 6 < sin(2 t ) , 1 > The speed is given by: v ( t ) = || v ( t ) || = 6 2 cos 2 (2 t ) + 6 2 sin 2 (2 t ) + 1 = 36(cos 2 (2 t ) + sin 2 (2 t )) + 1 = 37 The acceleration is given by: a ( t ) = v ( t ) = < - 12 cos(2 t ) , - 12 cos(2 t ) , 0 > 2. Find the distance between the planes with equations x + 2 y - z = 1 and x + 2 y - z = 13. Solution: We first need to identify a vector which is simultaneously per- pendicular to the two planes. By inspecting the equations, we see that such a vector is < 1 , 2 , - 1 > . Our plan is to find a line which is perpendicular to both planes and compute the distance between the points at which the line meets the two planes. In fact, we will choose the line in such a way that we already know its intersection with the first plane. This is quite simple: all we need is a point from the plane x + 2 y - z = 1, e.g. (1 , 0 , 0) (obtained by setting y = z = 0 and then letting x define itself through the equation of the plane).

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self quiz 3 answers - MATH 210 Self-quiz 3 1 Consider the...

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