Answer to Question #280076 in Analytic Geometry for abhi

Question

The equation of the plane passing through the point (1, –2, 4) and perpendicular to the line, whose direction ratios are 2, 4, –1 is

Answer 1

Equation of a plane perpendicular to a given vector $\vec n=\langle2, 4, -1\rangle$ and passing through a given point $(1, –2, 4)$ is

$$2(x-1)+4(y-(-2))+(-1)(z-4)=0$$

$$2x-2+4y+8-z+4=0$$

The equation of the plane passing through the point (1, –2, 4) and perpendicular to the line, whose direction ratios are 2, 4, –1 is

$$2x+4y-z+10=0$$