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

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