How to Find the Equation of a Plane with Three Given Points?

[dagg3r]

hi all I am struggling to on these types of questions ill post here

1. find the equation of the plane containing the points A(-1,2,1) B(0,2,3) and C(4,-1,2)

i tried to plot this on a x,y,z and maybe i rearranged to get formula n=CA * CB but its wrong heh no idea how to do this anyone can help me out thanks heapsss!

 

[blimkie]

use A and B to find vector AB and then find vector AC (AB = B - A and AC = C - A)

now the vector equation is in this form

(x,y,z) = ( a1, a2, a3 ) + s( ab1, ab2, ab3, ) + t(ac1, ac2, ac3)

from here you can find you parametric and symetric equations and further you can do find the cross product to find the normal vectors and find the scalar eqatuin in the form of Ax + By + cz + D = 0

look in the textbook

 

[HallsofIvy]

I presume you meant n= CA X CB where X is the cross product.

Show us what you did: what CA and CB are and how you did the cross product.