My apologies if a question like this already exists but I haven't been able to find anything. A point is given (1,4,5) and a perpendicular vector is also given (7,1,4). I am asked to find the parametric (vector) form of a plane using this information.
I understand that the parametric form is given by $\ \vec r=\vec r_0+s \vec u +t \vec v; \ s,t \ \epsilon \ \Bbb R$ and that in this case $\vec r_0$ will be (1,4,5). I was able to find the Cartesian equation to be $7x+y+4z=31$ and the answer for the parametric form is given as $\ \vec r=(1,4,5)+s(4,0,-7)+t(0,4,-1)$
I appreciate any help that anyone could give. Thanks