Write down an equation of the plane which passes through the point (−3,5,−1) that is perpendicular to the vector [−1,3,−9]. 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 · 2018-05-25T07:55:18

#-x+3y-9z=27#. See process and explanation below

Plane general equation is #Ax+By+Cz+D=0#

We know that in that form, the vector #(A,B,C)# is a perpendicular vector to plane given. Then

#-1x+3y-9z+D=0#

Now, however point #(-3,5,-1)# is a plane point, then

#-1·(-3)+3·5+9·1+D=0# and from here #D=-27#

Finally we have #-x+3y-9z-27=0# or #-x+3y-9z=27#