The equation of plane passing through three non collinear points(0,1,2),(1,0,-2) and (-2,1,0) is |
x−0
y−1
z−2
1−0
0−1
−2−2
−2−0
1−1
0−2
| = 0 |
x
y−1
z−2
1
−1
−4
−2
0
−2
| = 0 2x+10y−10−2z+4=0 2x+10y−2z−6=0The equation of the plane passing through the point (1,2,3) is a(x−1)+b(y−2)+c(z−3)=0 The plane is perpendicular to x+y+z=1. Therefore, a+b+c=0. Also, the plane is perpendicular to 2x−3y+z=5 Therefore, 2a−3b+c=0 Thus,