I have this equation:
$3x+5y+2z=20$
Of the plane $3x+5y+2z=20$ give two direction vectors that are perpendicular to each other.
I have used linear algebra and came up with the following parametric equation: $\left( 20/3,0,0\right)+t\left(-\dfrac 53,1,0\right)+u\left(-\dfrac 23,0,1\right)$
Is this a correct representation? I am not so sure.
so i have the two vectors $<-5/3,1,0>$ and $<-2/3,0,1>$ which if i take the dot product of with the normal vector $(3,5,2)$i will get zero thus the two vectors are perpendicular to the normal vector.