The distance between the line r → = 2 i ^ - 2 j ^ + 3 k ^ + λ i ^ - j ^ + 4 k ^ and the plane r…

The distance between the line r → = 2 i ^ - 2 j ^ + 3 k ^ + λ i ^ - j ^ + 4 k ^ and the plane r → . i ^ + 5 j ^ + k ^ = 5 is :
  1. 10 3 3
  2. 10 3
  3. 10 9
  4. None of these

Solution

Given line is

⇒     r → = 2 i ^ - 2 j ^ + 3 k ^ + λ i ^ - j ^ + 4 k ^         ...... (i)

and r → . i ^ + 5 j ^ + k ^ = 5         ..... (ii)

By i ⇒     { a → = 2 i ^ - 2 j ^ + 3 k ^ b → = i ^ - j ^ + 4 k ^

By ii ⇒     n → = i ^ + 5 j ^ + k ^

∵ b → . n → = 0

Therefore, the line is parallel to the plane. Thus, the distance between the line and the plane is equal to the length of the perpendicular from a point a → = 2 i ^ - 2 j ^ + 3 k ^ on the line to the given plane.

Hence, the required distance.

= 2 i ^ - 2 j ^ + 3 k ^ . i ^ + 5 j ^ + k ^ - 5 1 + 5 2 + 1

= 10 3 3

Asked in: MHT CET Full Test 11

Practice more Line and Plane questions on Aicharya