Find equation plane through the point P and perpendicular to

Find equation: plane through the point P and perpendicular to the line x+1/2 = y - 4 = 2z. Show your work, including which vectors you find, and the normal vector. Combine all constants in your answer. a rightarrow = -1, 0, 1/2, b rightarrow = 0, 2, 4 P = (1, 2, 0) Q = (1, 5, 0) R = (4, 6, 0) S = (3, 1, 0)

Solution

We have to find the equation of plane passing through P and perpendicular to line

Given that The point P(1,2,0) and

plane is perpendicular to the given line

{(x+1)/2}=y-4=2z

so the direction vecor of the line =<2,1,0.5>

since plane perpendicular to the line so the normal vector for plane is the direction vector of line

Normal vector=<2,1,0.5>

then equation of plane

(r-p).N=0

(r - <1,2,0>).<2,1,0.5>=0

(x-1,y-2,z-0).(2,1,0.5)=0

2(x-1)+(1(y-2)+0.5(z)=0

2x+y+0.5z-2-2=0

by multiplying 2

4x+2y+z=8

This the required equation of plane.