I am given the following vectors :
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:ℝ3 → ℝ3 which projects points orthogonally onto the plane containing p, q and r.
equation for a normal to a plane:
f(x,y,z) = ax + by + cz + d = 0
projvn = (|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.