Calc 3 Quiz 2

# Calc 3 Quiz 2 - Instructor Dr Yuli B Rudyak MAC 2313...

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Instructor: Dr. Yuli B. Rudyak MAC 2313, Calculus 3 with Analytic Geometry, Fall 2011 QUIZ 2, SEPTEMBER 21, 2011 Problem 1. Find parametric equations for the line through A (5 , 1 , 0) that is perpendicular to the plane 2 x - y + z = 1. In what points does this line intersect the coordinate planes? Solution: The direction vector of the target line is the normal vector of the given plane. So, we know the point (5,1,0) on the line and its normal vector h 2 , - 1 , 1 i and get the following parametric equations of the line x = 5 + 2 t , y = 1 - t , z = t . To ﬁnd intersection point of the line and the coordinate plane x = 0, put x = 0 in the equation x = 5 + 2 t and get t = - 5 / 2. Then y = 1 - t = 7 / 2 and z = t -- 5 / 1. So, we get the intersection points (0 , 7 / 2 , - 5 / 2. The remaining case can be considered similarly. Answer: for y = 0 we have (7,0,1), for z = 0 we have (5,1,0). Problem 2. Find parametric equations for the line through the point A (0 , 1 , 2) that is perpendicular to the line

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Calc 3 Quiz 2 - Instructor Dr Yuli B Rudyak MAC 2313...

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