Practice Problems Ch. 15

Question 1

Find the integral when you are given a tetrahedron and the points of its vertices.

Answer 1

1. Use the Vertices to draw the tetrahedron.
2. Then you can use the vertices to find two lines of the Plane that the tetrahedron is bounded by. Thus AB, BC. Just add the vector values for this.
3. Find Cross Product of the Two lines to get the normal vector of this plane. Cross product is determinant with I, j, k.
4. Then you have your plane that bounds this integral. Just take a point in the plane (u, v, w) and make equation
   (x- u)i + (y - v)j + (z - w)k = 0
5. Break The tetrahedron into two planes

Question 2

Find a vector between two points
A = <a>
B = < x, y, z></a>

Find AB
Find BA</a>

Answer 2

AB = < x-a, y-b, z-c>

BA = < a-x, b-y, c-z>