Math 1320 Lab 7
Name/Unid:
1. Find the equation of the plane that passes through A = (−1, 0, 0), B = (0, −2, −1) and
C = (2, 0, 1). Is the point (1, 1, 1) on the plane? If not, find the distance from the point
to the plane.
2. (a) Find the point at which the given lines intersect:
r = h1, 1, 0i + th1, −1, 2i
r = h2, 0, 2i + sh−1, 1, 0i
(b) Find the equation of the plane that contains both lines.
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3. A uniform solid cylinder of radius r = 1.2 m is pulled along a horizontal surface by a
cord wrapped around it. The cylinder rolls without slipping on the surface. Suppose
it is pulled with a constant force F = 10 N with an angle of π/3 with respect to the
horizontal.
(a) Find the work done by the force to displace the cylinder a distance of 3m.
(b) Find the magnitude of the torque about the center of the cylinder, and state the
direction of the torque.
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4. A parallelepiped is generated by three vectors a = h2, 0, 0i, b = h−2, 2, 0i and c =
h1, −1, 2i, as shown in the graph.
(a) Find the area of the bottom face ABCD.
(b) Find the volume of the parallelepiped.
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(c) Using the given vectors, compute the vector representations of AB 0 and AD0 .
(d) Are AB 0 and AD0 orthogonal, parallel, both, or neither?.
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5. (a) Write the equation in spherical coordinates:
x2 − 2x + y 2 + 2y + z 2 = 0.
(b) Write the equation in rectangular coordinates. What’s the name of this surface?
r2 3 2 2
z=
+ r sin θ.
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