Answer: 2x+y+z=7.
- A 2x+y+z=5
- B x+2y+z=7
- C 2x-y+z=7
- D 2x+y+z=7
Correct answer: D. 2x+y+z=7
Explanation: AB = (1,-2,0), AC = (2,-3,-1). Normal = AB x AC = |i j k; 1 -2 0; 2 -3 -1| = i(2-0)-j(-1-0)+k(-3+4) = (2,1,1). Plane through A(2,2,1): 2(x-2)+1(y-2)+1(z-1)=0, giving 2x+y+z=7.
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