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 March 28th, 2016, 10:02 AM #1 Newbie   Joined: Mar 2016 From: Canada Posts: 24 Thanks: 0 Determine a scalar equation Determine a scalar equation for the plane that passes through the point (2,0,âˆ’1) and is perpendicular to the line of intersection of the planes 2x + y â€“ z + 5 = 0 and x + y + 2z + 7 = 0. I know that the line of intersection is in both planes, so its direction vector must be perpendicular to both normal vectors (2, 1, -1) and (1, 1, 2). But I'm not sure where to go from there. Last edited by skipjack; March 28th, 2016 at 01:26 PM. March 28th, 2016, 12:03 PM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 And that direction vector must be perpendicular to the desired plane. A plane with normal vector , containing point $\displaystyle (x_0, y_0, z_0)$ has equation $\displaystyle A(x- x_0)+ B(y- y_0)+ C(z- z_0)= 0$. Thanks from puppypower123 March 28th, 2016, 01:21 PM   #3
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 Originally Posted by puppypower123 I know that the line of intersection is in both planes, so its direction vector must be perpendicular to both normal vectors (2, 1, -1) and (1, 1, 2). But I'm not sure where to go from there.
The vector cross product $\vec a \times \vec b$ is a vector that is perpendicular to both $\vec a$ and $\vec b$.

Last edited by skipjack; March 28th, 2016 at 01:27 PM. March 28th, 2016, 01:29 PM #4 Newbie   Joined: Mar 2016 From: Canada Posts: 24 Thanks: 0 So would i place it like this to get the solution? A(2âˆ’1)+B(1âˆ’1)+C(-1âˆ’2)=0 March 28th, 2016, 01:34 PM #5 Newbie   Joined: Mar 2016 From: Canada Posts: 24 Thanks: 0 Oh wait! I understand! I use both! nâƒ— =nâƒ— 1Ã—nâƒ— 2=(2,1,âˆ’1)Ã—(1,1,2)=(3,âˆ’5,1) (xâˆ’2,y,z+1).(3,âˆ’5,1)=0 â‡’ 3x âˆ’ 5y + z = 5 Last edited by skipjack; March 28th, 2016 at 02:22 PM. March 28th, 2016, 02:14 PM #6 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,696 Thanks: 2681 Math Focus: Mainly analysis and algebra That looks OK to me. March 31st, 2016, 09:50 AM   #7
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Quote:
 Originally Posted by puppypower123 So would i place it like this to get the solution? A(2âˆ’1)+B(1âˆ’1)+C(-1âˆ’2)=0
A(x- 1)+ B(x- 1)+ C(x- 2)= 0. Tags determine, equation, scalar ### determine the scalar equation

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