Let P be the plane \(x + y + z = 0. \)
a) Find a vector lying in the plane.
b) Find a vector that is orthogonal to the plane (normal)
Thanks in advance!
+130099 We have that
x + y + z = 0
We need two vectors in the plane to find an orthogonal vector
The points (1, 1, - 2) , (0, 1, -1) and (6,-6, 0) will lie in the plane
One vector lyimg in the plane will be ( 0-1, 1 -1 , -1 - -2) = (-1, 0, 1) = -1i + 0j + 1k
Another will be ( 6 - 1, -6,-1, 0 - -2) = ( 5, -7, 2) = 5i - 7j + 2k
We can use the cross-prduct to find a vector normal to the plane
i j k i j
-1 0 1 -1 0
5 -7 2 5 -7
[ (0*2)i + (1*5)j + (-1*-7)k ] - [(5*0)k + (-7*i)i + (2*-1)j ] = 7i + 7j + 7k
