Find an equation for the plane M that contains the point P and that is parallel to u and to v. Give the equation in the form ax + by + cz = d.

Question

I'm asked to: find an equation for the plane M that contains the point P and that is parallel to u and to v. Give the equation in the form ax + by + cz = d.

Here is what is given: Define P(1,0,−1) and the vectors u = <3,−1,2> and v = <−1,1,−1>.

I had to calculate the cross product of u*v at the previous question.

Answer 1

Hint: The crossproduct is given by $$\vec{u}\times \vec{v}=[-1,1,2]$$ So we have found the cooefficients of the plane $$-x+y+2z+d=0$$ Plugging $$x=1,y=0,z=-1$$ in this equation we will find $d$.