Answer
Let $(x_0,y_0,_0)$ be a point on the line and $ \lt a,b,c\gt$ be a direction vector of the line.
Equation of the line is given by $r=r_0+tv$
Then a vector equation of the plane is $ \lt a,b,c\gt. (x-x_0,(y-y_0),(z-z_0)$
A scalar equations is represented as: $a(x-x_0)+b(y-y_0)+c(z-z_0)=0$
Work Step by Step
Let $(x_0,y_0,_0)$ be a point on the line and $ \lt a,b,c\gt$ be a direction vector of the line.
Equation of the line is given by $r=r_0+tv$
Then a vector equation of the plane is $ \lt a,b,c\gt. (x-x_0,(y-y_0),(z-z_0)$
A scalar equations is represented as: $a(x-x_0)+b(y-y_0)+c(z-z_0)=0$
