Finding Equation of Plane by Point and Normal Vector

Example

• With point $(2,4,-1)$
• With normal vector $n=(2,3,4)$ $n=\frac{(2,3,4)}{(A,B,C)}$ $P_o=\frac{(2,4,-1)}{(x_0,y_0,z_0)}$ Then we get:
• $2\ast (x-2)+3(y-4)+4(z+1)=0$
• $⟹2x-4+3y-12+4z+4=0$
• $⟹2x+3y+4z-12=0$ We also have intercepts at $(6,0,0),(0,4,0),(0,0,3)$