UPSEE Solved Model Paper 1

The equation of plane passing through (1, 1, 2) is
A(x - 1) + B(y - 1) + c(z - 2) = 0 ...(i)
Now, It is perpendicular to x - y + 2 = 2 and
x + y - 2z = 4.
∴ A - B + C = 0
A + B - 2c = 0
⇒

A

| −1 1 1 −2 |

=

B

| 1 1 −2 1 |

=

C

| 1 −1 1 1 |

Substitute the value of A, B and c is equation (1)
1(x - 1) + 3(y - 1) + 2(z - 2) = 0
⇒ x + 3y + 2z = 8
Distance of this plane form (2, 2, 1) is given by
d = |

2+2.3+2.1−8

√(1)2+(2)2+(2)2

|
d =

2

√14