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 $-x+3y-9z=27$