UPSC NDA Math Model Paper 7

Given:

x+1

1

=

y−1

2

=

z−2

2

Direction ratio of line = (1, 2, 2)
Equation of plane is 2x−y+√λz+4=0
Direction ratio of normal to the plane =(2,−1,√λ)
sin θ=

1

3

Now,
sin‌θ=|

1×2+2×−1+2×√λ

√12+22+22√22+(−1)2+(√λ)2

|
⇒

1

3

=|

2√λ

3×√5+λ

|
⇒|√5+λ|=|2√λ|
Squaring both sides, we get
⇒5+λ=4λ⇒3λ=5∴λ=

5

3