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 July 7th, 2015, 01:44 PM #1 Newbie   Joined: Jul 2015 From: canada Posts: 1 Thanks: 0 Scalar Equation of a Plane Determine a scalar equation for the plane through the points M(1, 2, 3) and N(3 ,2, -1) that is perpendicular to the N plane with equation 3x + 2y + 6z + 1 = 0. I get that Ax + By + Cz + D = 0 is needed but im doing e learning and am really not sure how to apply it to solve this question July 7th, 2015, 03:29 PM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 The plane 3x+ 2y+ 6z+ 1= 0 has normal vector of the form 3i+ 2j+ 6k. The normal vector to the plane Ax+ By+ Cz+ D= 0 is of the form Ai+ Bj+ Ck and must be perpendicular to the first normal vector. That is, we must have 3A+ 2B+ 6C= 0. The fact that M(1, 2, 3) is in the plane means that we must have A(1)+ B(2)+ C(3)+ D= A+ 2B+ 3C+ D= 0. The fact that N(3, 2, -1) is in the plane means that we must have A(3)+ B(2)+ C(-1)+ D= 3A+ 2B- C+ D= 0. So we have 3A+ 2B+ 6C= 0, A+ 2B+ 3C+ D= 0, and 3A+ 2B- C+ D= 0. That is only three equation but if we were to multiply or divide each number in Ax+ By+ Cz+ D= 0 we would have an equivalent equation so an equation for that same plane. That means that we could, for example, take D= 1 and have three equations to solve for A, B, and C. July 7th, 2015, 03:30 PM   #3
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 Originally Posted by holdyuh Determine a scalar equation for the plane through the points M(1, 2, 3) and N(3 ,2, -1) that is perpendicular to the N plane with equation 3x + 2y + 6z + 1 = 0. I get that Ax + By + Cz + D = 0 is needed but i'm doing e learning and am really not sure how to apply it to solve this question
Dividing by $\displaystyle D$ you get

$\displaystyle \dfrac{Ax}{D}+\dfrac{By}{D}+\dfrac{Cz}{D}+1=0$

Now let $\displaystyle P=\dfrac{A}{D}$, $\displaystyle Q=\dfrac{B}{D}$, $\displaystyle R=\dfrac{C}{D}$ so your plane becomes

$\displaystyle Px+Qy+Rz+1=0$

You can now get three equations (for your three unknowns $\displaystyle P,Q,R$ by using the two given points and taking the dot product of the normals to the planes. Your final answer should be $\displaystyle 2x-6y+z+7=0$. Tags calcus, equation, homework help, physics or calc, plane, scalar Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post miguelogy Linear Algebra 4 October 15th, 2013 01:34 PM aaron-math Calculus 2 March 7th, 2012 01:01 AM maximus101 Trigonometry 1 March 11th, 2011 07:38 AM remeday86 Calculus 1 April 7th, 2009 03:23 AM veronicak5678 Calculus 5 March 12th, 2009 06:52 PM

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