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 $\displaystyle ax+by+cz+d=0$ for the plane containing the above vectors, and then $\displaystyle (a,b,c)$ is normal to each and every once of them.
Way 2: (this is a slight variation of the above): let $\displaystyle \overrightarrow{AB}=(-3,1,-1)\,,\,\overrightarrow{AC}=(5,2,-9)$ , and now calculate the vector $\displaystyle (-3,1,-1)\times (5,2,-9)$ , which is normal to the plane generated by $\displaystyle \overrightarrow{AB}\,,\,\overrightarrow{AC}$ .
Tonio