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 <A, B, C>, containing point $\displaystyle (x_0, y_0, z_0)$ has equation $\displaystyle A(x x_0)+ B(y y_0)+ C(z z_0)= 0$. 
March 28th, 2016, 01:21 PM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,696 Thanks: 2681 Math Focus: Mainly analysis and algebra  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 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902  

Tags 
determine, equation, scalar 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Scalar Equation of a Plane  holdyuh  PreCalculus  2  July 7th, 2015 04:30 PM 
determine the equation  shawen  Calculus  1  July 23rd, 2014 05:01 PM 
Determine equation given a table of values  dendimiiii  Applied Math  1  February 12th, 2014 09:18 AM 
Determine a equation HELPP!!!!  livestrong136  Calculus  2  May 5th, 2012 01:42 PM 
Determine Equation  RMG46  Algebra  12  July 5th, 2010 05:00 PM 