Before you start solving your problem. open Calcl'lot3d, click on Add to Graph and select Space Curve. Check the box next to the curve, then uncheck it. You can proceed now with your problem {ignore this curve from now on. but do not erase it -this is done because of a bug in the program}. Consider the equation the tetrahedron whose sides are the 3 coordinate planes and the plane I. y z ++=L a b c 1. ill-"here are the vertices of this tetrahedron? How many edges does it have? 1Write the vectors that correspond exactly to these edges. (This will help you plot it later on}. 2. Compute the volume of the tetrahedron using either a double or a triple integral. Your answer should depend on c. b. c. 3. Read pages 928930 in the textbook. Explain the difference between the center of mass and the centroid of a 3 dimensional object. 4. Compute the E coordinate of the centroid. After this. explain in words how we can determine the value of the other two coordinates T. 3 of the centroid. without actually computing anything. 5. Now. assume that the density of the tetrahedron is (an-y. z) = z. "-"hat is the mass of the tetrahedron? (You should be able to answer this question without computing anything, only using your work from (4)). [5. If we have two tetrahedra with the same vertices. one with density Eln-y. z} = 1 and the other with density 6(11, 3;, a} = 2:, which values of a, b, c will ensure that they both have the same mass? The answer to this question will be a relation involving c.b.c. For which values of c. b, c will the second tetrahedron have bigger mass? 7. Choose concrete positive values for c. b, c so that the two tetrahedra have the same mass. Plot the tetrahedron for this values: Choose "Vector" and enter the vectors corresponding to all the edges, with initial points at the corresponding vertices. Plot the centroid in red. Take a screenshot