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Question

Find an equation of the plane that contains the line

          x = −9−t ,    y = −4+6 t ,    z = 2−t

and is parallel to the plane −8 x−4 y−16 z = 4.

Leave your answer in the form A x + B y + C z = D, where A, B, C are integers.

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Answer 1 · 2018-05-25T09:29:39

#2x+y+4z=14#. See below

If plane is parallel to #-8x-4y-16z-4=0#, then our plane is

#-8x-4y-16z+D=0# because both have the same normal vector #(-8,-4-16)=-4·(2,1,4)#

Note that the given plane is equivalent to #2x+y+4z-1=0#

And parallel plane is #2x+y+4z+D=0#

Line given can be writen as #(x+9)/-1=(y+4)/6=(z-2)/-1#

Then the singular point #(-9,-4,2) in# plane

Then #2·(-9)-4+8+D=0#

#D=14#

Then our plane is #2x+y+4z=14#

Find an equation of the plane that contains the line

`x = −9−t , y = −4+6 t , z = 2−t`

and is parallel to the plane −8 x−4 y−16 z = 4.

Leave your answer in the form A x + B y + C z = D, where A, B, C are integers.