e110k - MAC 2313 Exam I and Key Sept 16, 2010 Prof. S....

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MAC 2313 Sept 16, 2010 Exam I and Key Prof. S. Hudson 1) [10 pts] Find the distance from the point P (1 , 1) R 2 to the line y = 2 x + 1. Hint: compute a normal vector and a scalar projection. 2) [10 pts] Show that these lines intersect and find the point of intersection. Note: the values of t in L 1 and L 2 do not have to match. L 1 : x = 1 + t,y = 1 + t,z = 1 + 2 t L 2 : x = 2 + t,y = 3 ,z = 4 + t 3) [10 pts] Find two unit vectors in R 2 parallel to the line y = 3 x + 1. 4) [15 pts] Find the equation of the plane that passes through the points P (1 , 1 , 0), Q (1 , 0 , 2) and R (0 , - 1 , 1). 5) [10 pts] Convert this equation from spherical coordinates to rectangular coordinates and sketch the graph. Hints: We did a similar problem in class. One idea is to multiply both sides by ρ first, and then use conversion formulas, such as y = ρ sin φ sin θ , though the formula for z might be more useful here. ρ = 4 cos( φ ) 6) [10 pts] Find an equation for the trace of 4 x 2 + y 2 + z 2 = 9 in the plane y = 2. State what kind of conic section the trace is [is it a parabola? etc].
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This note was uploaded on 12/27/2011 for the course MAC 2313 taught by Professor Grantcharov during the Fall '06 term at FIU.

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e110k - MAC 2313 Exam I and Key Sept 16, 2010 Prof. S....

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