Vector equation of plane $3x − 5y + 2z = 1$ in $\mathbb{R}^{3}$

Question

Vector equation of plane $3x − 5y + 2z = 1$ in $\mathbb{R}^{3}$

It seems like it shouldn't be that difficult, but it's completely stumped me. Nothing on this exact format of question in lecture notes or in the textbook. If anybody can explain how one gets the vector equation from the formula of a 3D plane, it would be much appreciated, thanks.

Answer 1

HINT

• find three not collinear points $P,Q,R$ on the plane
• the parametric equation is: $$P+t(Q-P)+s(R-P)$$