advertisement

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. Page 2 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. Page 3 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. Page 4 (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?. Page 5 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. 4 4 Page 6