Homework # 3 - Math 250
The problems on this homework must be done alone. The honor code is in effect.
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In problems 1 through 3, let A = (1,1,1), B = (5,3,2), C=(2,5,3), and D=(3,2,5).
1. Consider the parallelepiped with vertices at A, B, C, and D, such that B, C, and D are all adjacent to A (That is, there is an edge between A and B, between A and C, and between A and D). Find the coordinates of the vertex in the parallelepiped opposite to A.
a. (6, 7, 4)
b. (8, 8, 8)
c. (7, 4, 6)
d. (3, 5, 6)
e. (6, 7, 5)
2. Find the volume of the parallelepiped mentioned in number 1.
a. 7
b. 49/3
c. 49/2
d. 49
e. 56
3. Find the volume of the tetrahedron with vertices at A, B, C, and D.
a. 49/6
4. Find an equation of the plane through the points (1, 1, 1), (2, 2, 0), and (3, 0, 1). Example 3 in the section 11.5 may help.
a. x - y = 0
b. x + 2y + 3z = 6
c. x + y - z = 1
d. 2x - y = 1
e. x - y + z = 0
5. Find the area of parallelogram ABCD.
a. 9√3/2
b. 6√3
c. 15√3/2
d. 9√3
e. 21√3/2
6. Find the area of triangle ABC.