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Explain why there is no plane parallel to the plane... (see description)?
Explain why there is no plane parallel to the plane 5x-3y+2z=10 that contains the line with parametric equations x=t-4, y=3t-2, z=5-2t
I can't seem to see the existence of this plane.
1 Answer
- az_lenderLv 77 years agoFavorite Answer
A vector parallel to the given line runs from (-4,-2,5) to (-3,1,3).
The vector is i + 3j - 2k.
A vector perpendicular to the given plane, and to ALL planes
parallel to it, is 5i - 3j + 2k.
But that vector isn't perpendicular to (i + 3j - 2k), because their
dot product isn't zero. So the line doesn't lie in any of the
planes parallel to the given plane.
