MATH 251 Multivariable Calculus Questions There are 3 questions.Please, solve these problems on your own paper, using one piece of paper perproblem. Write

MATH 251 Multivariable Calculus Questions There are 3 questions.Please, solve these problems on your own paper, using one piece of paper perproblem. Write neatly and clearly. If your work is scattered and/or difficult to follow, you maylose points, because when solving systems of equations this way, notation and organization are important. Math 251
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Homework: Sections 12.5
1. Find parametric equations for the line passing through the center of the spheres.
Hint: Complete the square three times to rewrite the equations of the spheres so they are in
the form (x − h)2 + (y − k)2 + (z − l)2 = r2 .
x2 + y 2 + z 2 − 2x − 4y + 4z = 8
x2 + y 2 + z 2 + 2x + 6y + 4z = 20
2. Find an equation for the plane determined by the following two lines.
r1 (t) = h2, −3, 6i + th1, 1, 1i
r2 (t) = h−1, −6, 3i + th2, 0, −1i
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3. For each case below, create a pair of lines that meet the given condition(s). Show work to
prove that your pair of lines work:
(a) The lines are orthogonal and intersect.
(b) The lines are not orthogonal and intersect.
(c) The lines are parallel and do not intersect.
(d) The lines are skew.
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