Answer: (0,1,-1).
- A (0,1,-1)
- B (1,1,0)
- C (0,-1,1)
- D (1,-1,0)
Correct answer: A. (0,1,-1)
Explanation: Vectors in plane: v<sub>1</sub>=(1,0,0), v<sub>2</sub>=(0,1,1). Normal = v<sub>1</sub> x v<sub>2</sub> = |i j k; 1 0 0; 0 1 1| = i(0-0)-j(1-0)+k(1-0) = (0,-1,1). Alternatively, (0,1,-1) points the same axis. Using (0,-1,1): plane is 0*x-y+z=0, i.e., -y+z=0. Check (0,0,0): 0=0. Check (1,0,0): 0=0. Check (0,1,1): -1+1=0. So normal is (0,-1,1) or equivalently (0,1,-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