Answer to Question #212264 in Analytic Geometry for Moe

Question #212264

Which of the following planes are parallel to the line with equation r=(3,0,1)+λ(3,2,1)r = (3,0,1) + \lambda(3,2,-1)

  1. 2x3y=62x - 3y = 6
  2. xy+z=6x - y+z=6
  3. x27+z=6x - 27 + z = 6
  4. 3y+z=63 y + z = 6
1
Expert's answer
2021-07-01T05:48:53-0400

A line and plane are parallell if the dot product of direction vector of the line and normal vector of the plane is zero.


Direction vector of given line is <3,2,-1>

Option1: normal vector is <2,-3,0>

<3,2,-1>.<2,-3,0>=6-6+0=0

Option2: normal vector is <1,-1,1>

<3,2,-1>.<1,-1,1>=3-2-1=0

Option2: normal vector is <1,0,1>

<3,2,-1>.<1,0,1>=3-1=2

Option2: normal vector is <0,3,1>

<3,2,-1>.<0,3,1>=6-1=5


Hence, options 1 and 2 are correct.



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