Math 2374 Review of some material about vectors.

One section of the roof of a house has a rectangular hole in it. In some coordinate system, the vertices of this rectangular hole are (4,5,6), (5,7,9), (5,3,7) and (6,5,10).

1.
Prove that this hole really has a rectangular shape.

2.
Find the area of the hole. (Assume that all units are
in inches.

3.
This section of the roof forms part of a plane. Show that the equation of this plane is
4x+y-2z = 9

4.
Find a vector **n**
which is normal to this plane. Choose a
normal which points down into the house.

It is raining at the rate of 2 inches per hour.
Because of the wind, the rain does not fall straight down, but rather in
the direction of the vector **v** = (1,4,-9).

5.
Find the projection of **v** onto **n**. (In Math 1372, this was called the vector
projection)

6.
Find the component of **v** in the direction of **n**. (In Math 1372, this was called the scalar
projection.)

7. At what rate is the rainwater flowing through the window? Your answer should be in cubic inches per hour.