Answer: x-y+z=1.
- A 2x-y-z=2
- B x-y+z=0
- C x-y+z=1
- D x+y+z=1
Correct answer: C. x-y+z=1
Explanation: The line passes through (1,0,0) with direction (2,1,-1). For the plane to also be parallel to i+j = (1,1,0), its normal must be perpendicular to both directions: normal = (2,1,-1) x (1,1,0) = (1*0-(-1)*1, (-1)*1-2*0, 2*1-1*1) = (1,-1,1). Plane through (1,0,0) with this normal: 1(x-1)-1(y-0)+1(z-0)=0, giving x-y+z=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