Answer: y + 2z = 3.
- A y + 2z = 3
- B x - y + z = 0
- C y - z = 1
- D x + y = 2
Correct answer: A. y + 2z = 3
Explanation: Family: (x+y+z-1)+k(2x+3y+4z-5)=0. Coefficient of x = 1+2k = 0, so k = -1/2. Plane: 0*x + (1-3/2)y + (1-2)z = 1-5/2, giving (-1/2)y + (-1)z = -3/2, so y + 2z = 3.
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