I broke my problem into five parts.

I'd like to post my solutions as well 'cause I want to increase my confidence with these types of problems. Also, I'd like to check if I made any errors.

Cheers.

A triangle is made by points P = (1, 1, 2), Q = (-1, 0, 3), R = (2, 1, -1).

1. Projection ofPQontoPR?

PQ= <-2, -1, 1>,PR= <1, 0, -3>

Projection vector is <-1 / 2, 0, -3 / 2>

2. Find at least one unit vector orthogonal to the plane made by the three points of the triangle.

PQxPR= <3, -5, 1>

Unit vector is <3 / 35^(1/2), -5 / 35^(1/2), 1 / 35^(1/2)>

3. Area of triangle PQR?

A = 0.5 * ||PQxPR||

A = 35^(1/2) / 2

4. Find two forms of the equation of line l going through point P and perpendicular to the triangle PQR.

Vector: <x, y, z> = <1, 1, 2> + t<3, -5, 1>

Parametric:

x = 1 + 3t, y = 1 - 5t, z = 2 + t

5. What's the general form of the plane going through the triangle points P, Q, R?

3x - 5y + z = 0

I used the point (1, 1, 2) and the normal vector <3, -5, 1> to get this equation.