MATH 241 Spring 2011 Midterm 1 Solutions - Math 241 Exam I...

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Math 241 Exam I Solutions Prof. Joshua Cooper, Spring 2011 1. What is the equation of the sphere with center (1 , 2 , 3) which passes through the point (0 , 4 , 1)?
2. Find the point of intersection and the angle between the line whose parametric equation is r ( t ) = h 5 t + 3 , - t, 2 t - 1 i and the plane given by 2 x - y + z = 4.
between the line and the plane is given by cos θ = h 5 , - 1 , 2 i·h 2 , - 1 , 1 i kh 5 , - 1 , 2 iik·kh 2 , - 1 , 1 ik = 5 · 2 + ( - 1) · ( - 1) + 2 · 1 25 + 1 + 4 · 4 + 1 + 1 = 10 + 1 + 2 30 · 6 = 13 6 5 = 13 5 30 . Therefore, the angle θ is given by θ = cos - 1 13 5 30 ! .

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