Show that the line l given by: x=2+t, y=-2+t, z=-1+t and the plane 2x-3y+z-2=0 do not intersect.

Darryl English

Darryl English

Answered question

2022-07-27

Show that the line l given by: x=2+t, y=-2+t, z=-1+t and the plane 2x-3y+z-2=0 do not intersect.

Answer & Explanation

Bubbinis4

Bubbinis4

Beginner2022-07-28Added 8 answers

Plug in the parameterized components of the line into the equation of the plane to see if they intersect:
2(2 + t) - 3(-2 + t) + (-1 + t) - 2 = 0
Distribute:
4 + 2t + 6 - 3t - 1 + t - 2 = 0
Simplify:
7 = 0 HOWEVER, we all know that 7 0, so this means the given line and plane do NOT interesect at any point is space.

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