# Thread: Help! Equations of Planes and Lines

1. ## Help! Equations of Planes and Lines

Hi im having problems with these questions:

Q1. Find the equation of the plane which contains points (2,-1,4), (3,2,-1) and perpendicular/orthogonal to the plane x + y + 2z = 3.

Q2. Find the equation of the plane containing the point (3,-1,-5) and perpendicular/orthogonal to the planes 3x - 2y + 2z = -7 and 5x - 4y + 3z = -1.

Explanation, answers and steps would be appreciated,

thanks

Moon

2. Originally Posted by Moon Hoplite
Hi im having problems with these questions:

Q1. Find the equation of the plane which contains points (2,-1,4), (3,2,-1) and perpendicular/orthogonal to the plane x + y + 2z = 3.

Q2. Find the equation of the plane containing the point (3,-1,-5) and perpendicular/orthogonal to the planes 3x - 2y + 2z = -7 and 5x - 4y + 3z = -1.

Explanation, answers and steps would be appreciated,

thanks

Moon
1. The vector (1,1,2) is normal to the plane. Then you can take one of the points and add them together. Then find the plane that contains the three points.

3. hmmn i got the answer x+ y + 2z = 9, is this correct?

i used the: a(X-Xo) + b(Y-Yo) + c(Z-Zo) = 0 rule,

using n = 1 1 2

Xo= 2
Yo = -1
Zo = 4 ........... from the point (2 -1 4)