Question

How far is the
point
(1,1,4) from the line of
intersection of the planes
x+y+z = 4, 2x+y-z = -4​

Answer 1

Answer:

SteEquation of plane passing through the intensction of 2 plane is given by

p  

1

​  

+λp  

2

​  

=0

⇒ (x+y+z−1)+λ(2x+y−3z+2)=0

x(2λ+1)+y(λ+1)+z(1−3λ)+(2λ−1)=0

This plane also passes through (1,1) substituting (1,1,1) in the above equation  

we get

x(−1)+y(−1+1)+z(1+3)+(−2−1)=0

−x+4z=3

x−4z=−3

orx−4z+3=0, which is the required equation of the plane of theplane