Answer: x-4y+2z=-1.
- A x-4y+2z=-1
- B x-4y+2z=1
- C x+4y-2z=1
- D 2x-3y+z=2
Correct answer: A. x-4y+2z=-1
Explanation: AB=(2,2,3), AC=(-2,-1,-1). Normal = AB x AC = |i j k; 2 2 3; -2 -1 -1| = i(2*(-1)-3*(-1))-j(2*(-1)-3*(-2))+k(2*(-1)-2*(-2)) = i(-2+3)-j(-2+6)+k(-2+4) = (1,-4,2). Plane through (1,0,-1): 1(x-1)-4y+2(z+1)=0, giving x-4y+2z=-1.
Three mutually perpendicular axes x, y, z meeting at the origin O, with a point P located by its (x, y, z) coordinates.
Concept context
Lines and planes in 3D space, direction cosines, distances, and angles