VITEEE 2015 Paper

Equation of plane passing through (2, 2, 1) is
a(x - 2) + b(y- 2) + c(z - 1) = 0 ....(i)
Since, above plane is perpendicular to
3x + 2y + 4z + 1 = 0
and 2x + y + 3z + 2 = 0
∴ 3a + 2b + 4c = 0 ....(ii)
and 2a + b + 3c = 0 ....(iii)
[Since for perpendicular a1a2 + b1b2 + c1c2 = 0]
On multiplying eq. (iii) by 2, we get 4a + 2b + 6c = 0 ....(iv)
On subtracting eq. (iv) from eq. (ii), we get
⇒ c = −

a

2

On putting c = −

a

2

in eq. (iii), we get b = −

a

2

On putting b = −

a

2

and c = −

a

2

in eq. (i),
we get a(x-2) −

a

2

(y - 2) −

a

2

(z - 1) = 0
⇒

a

2

[2 (x - 2) - (y - 2) - (z - 1)] = 0
⇒ 2x - 4 - y + 2 - z + 1 = 0
⇒ 2x - y - z - 1 = 0