# Math Help - a normal vector to the plane

1. ## a normal vector to the plane

this question is easy but i've forgotten how to answer it.

a plane contains the points A(0,1,5),B(-3,2,4) and C(5,3,-4).find a normal vector to the plane.

thank you.

2. Originally Posted by kokolily
this question is easy but i've forgotten how to answer it.

a plane contains the points A(0,1,5),B(-3,2,4) and C(5,3,-4).find a normal vector to the plane.

thank you.

Way 1 find a standard form $ax+by+cz+d=0$ for the plane containing the above vectors, and then $(a,b,c)$ is normal to each and every once of them.

Way 2: (this is a slight variation of the above): let $\overrightarrow{AB}=(-3,1,-1)\,,\,\overrightarrow{AC}=(5,2,-9)$ , and now calculate the vector $(-3,1,-1)\times (5,2,-9)$ , which is normal to the plane generated by $\overrightarrow{AB}\,,\,\overrightarrow{AC}$ .

Tonio