Given three points $a = (1,4,0), b=(2,1,5), c=(3,5,2)$ in $\mathbb{R^3}$, find each of the following
$iii)$ A parametric equation of the plane containing $a$, $b$ and $c$
My solution: $$(x,y,z) = (1,4,0) + t_{1}(2,1,5) + t_{2}(3,5,2)$$ $$x=1+2t_{1}+3t_{2}, \space\space y=4+t_{1}+5t_{2}, \space\space y=0+5t_{1}+2t_{2}$$
$iv)$ A Cartesian equation of the plain containing $a$, $b$ and $c$
My solution: I need a vector and a plane. Use $\vec{ab} = (1,-3,5)$ $$v = A(x-x_{0})+B(y-y_{1})+C(z-z_{0})$$ with perpendicular line
$v)$ A vector perpendicular to the plane containing $a$, $b$ and $c$
for iii) it must be $\vec{x}=(1,4,0)+t_1((2,1,5)-(1,4,0))+t_2((3,5,2)-(1,4,0))$ $\vec{x}=(1,4,0)+t_1(1,-3,5)+t_2(2,1,2)$