# Calc 3, finding planes that are parallel and perpendicular.

So I really need help with figuring out how to do this problem. I answered two of the questions (not sure if I am right) and I am just stuck on the 2nd part.

Questions: Two planes are given by the equations Q:2x+y−3z=2 and R:−x+2y−z=1.

Question 1: Find a vector normal to the plane Q. Find an equation of the plane which is parallel to Q and passes through the point (1,2,−1).

A vector normal to plane: <2,1,-3>

A normal vector for new plane is <2,1,-3>. A pt on plane is <1,2,-3>

T/f equation is

2(x-1) + 1(y-2) - 3(z+1) = 0

= (2x-2) + (y-2) - (3z+3) = 0

Question 2: Find a vector normal to the plane R. Find a vector equation of the line that is perpendicular to the plane R and passes through the point (0,0,−1).

Attempted Answer: Don't know how to start this one and help on how to start would be appreciated.

Question 3: Find a vector equation of the line in the intersection of Q and R.

• i j k
• 2 1 -3
• -1 2 -1

6i+5j+5k = 9.27

• For question 2, think about what “normal” means.
– amd
Commented Sep 14, 2018 at 5:28

Question 2 asks for a line normal to $R$ and passing through $(0,0,-1)$.
Thus your equation is $$r =(0,0,-1)+t(-1,2,-1)$$