- #1

- 3

- 0

## Homework Statement

I am given the following vectors :

Code:

```
p = 3 q = 2 r = 5
2 4 3
-4 -3 -1
```

1. a normal to the plane containing p, q and r.

2. the distance from the origin to the plane containing p, q and r

3. The distance from r to the line containing p and q

4. The matrix and translation of the affine transformation T:ℝ

^{3}→ ℝ

^{3}which projects points orthogonally onto the plane containing p, q and r.

## Homework Equations

equation for a normal to a plane:

f(x,y,z) = ax + by + cz + d = 0

projection equation:

proj

_{v}n = (|v . n|/|v|

^{2}) . v

## The Attempt at a Solution

I will have to edit this in since i need to leave quickly but I would still like to throw this out there, I know the equations, I know the normal is a vector which is orthogonal to the plane and thus who's dot product is equal to zero, but I do not know how to go about it.

As for #2 I do not know how to solve for an equation in which all vectors equal zero.

#3 I think the line containing p and q will be p - q = s, and i must project r onto s to find the distance

for #4 I do not understand what they are asking.