# Math Help - Help with a question about Planes

1. ## Help with a question about Planes

I cannot get the correct answer to this question..any help would be greatly appreciated. Thanks in advance

Let P1 be the plane defined by:
(-2,0,2), (5,-1,5) and (0,2,4)

Find the equation of the plane perpendicular to P1 and containing the line:
(x,y,z)=(0,-1,-3)+ t(-1,3,-3)

Answer should be in the form Ax+By+Cz-D=0

So first i found the equation for plane P1 as -8x-8y+16z-48=0
I do not really know where to go from here.
thanks

2. Originally Posted by kblythe
I cannot get the correct answer to this question..any help would be greatly appreciated. Thanks in advance

Let P1 be the plane defined by:
(-2,0,2), (5,-1,5) and (0,2,4)

Find the equation of the plane perpendicular to P1 and containing the line:
(x,y,z)=(0,-1,-3)+ t(-1,3,-3)

Answer should be in the form Ax+By+Cz-D=0

So first i found the equation for plane P1 as -8x-8y+16z-48=0
I do not really know where to go from here.
thanks

So dividing by -8 we get that $P_1:\,\,x+y-2z+8=0\,\Longrightarrow\,(1,1,-2)$ is a normal (and thus perpendicular) vector to $P_1$, so the wanted plane must contain, choosing t = 0 and t = 1 for the line, the vectors $(1,1,-2)\,,\,(0,-1,-3)\,,\,\,(-1,2,-6)$, so plugging this in $Ax+By+Cz+D=0$ and solving the system we get $A=-\frac{9}{5}C\,,\,\,B=\frac{2}{5}C\,,\,\,D=17$ , and the wanted plane is (taking $5C$) : $-9x+2y+5z+17=0$.

Check this

Tonio

3. hey thanks for the reply. the only part i am still confused about is that in the question it says it wants it in the form with minus D (Ax+By+Cy - D=0) and in your answer you have +17. Is that ok? or am i supposed to change my answer in some way to account for this?
thanks

4. Originally Posted by kblythe
hey thanks for the reply. the only part i am still confused about is that in the question it says it wants it in the form with minus D (Ax+By+Cy - D=0) and in your answer you have +17. Is that ok? or am i supposed to change my answer in some way to account for this?
thanks
Then multiply the entire equation by -1! $-1(-9x+2y+5z+17)=-1(0)$ so 9x- 2y- 5z- 17= 0.