Fall 2007 - Cioaba's Class - Quiz 2

# Fall 2007 - Cioaba's Class - Quiz 2 - Name Discussion...

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Name: PID: Discussion Section No: Time: TA’s name: Quiz 2, Math 20C - Lecture D (Fall 2007) Duration: 20 minutes Please close all your notes and books, turn off your phones and put them away. To get full credit you should support your answers. 1. (5 points) Find a parametric equation for the tangent line to the curve with the parametric equation x = e - t cos t,y = e - t sin t,z = e - t at the point (1 , 0 , 1). Solution. For t = 0, the point on the curve is ( e 0 cos 0 ,e 0 sin 0 ,e 0 ) = (1 , 0 , 1). The direction of the tangent line to the curve x = e - t cos t,y = e - t sin t,z = e - t is given by the value of vector ( dx dt , dy dt , dz dt ) (1) when t = 0. The direction (1) is ( dx dt , dy dt , dz dt ) = ( e - t ( sin t cos t ) ,e - t ( sin t + cos t ) , e - t ) (2) When t = 0, this equals (− 1 , 1 , 1 ) . Thus, the tangent line at (1 , 0 , 1) has direction (− 1 , 1 , 1 ) . The parametric equation of the tangent line at (1 , 0 , 1) is x 1 = t,y = t,z 1 = t which is the same as x = 1 t,y = t,z = 1 t.

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2. (5 points) Find an equation of the plane that passes through the point ( 1 , 2 , 1) and
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