QJEEAdv20Maa42c: JEE Advanced 2020 Mathematics - Class 12 JEEAdv20Maa42c Solution: Let α 2 + β 2 + γ 2 ≠ 0 and α + γ = 1. Suppose the point (3, 2, …

Question

Verified Solution • 2025–26 Session moderate

Let

α

² +

β

² +

γ

²

\neq

0 and

α

+

γ

= 1. Suppose the point (3, 2,

-

1) is the mirror image of the point (1, 0,

-

1) with respect to the plane

α

x +

β

y +

γ

z =

δ

. Then which of the following statements is/are TRUE?

Accepted Answer

Since, the point A(3, 2,

-

1) is the mirror image of the point B(1, 0,

-

1) with respect to the plane

α

x +

β

y +

γ

z =

δ

, then

\frac{α}{3 - 1} = \frac{β}{2 - 0} = \frac{γ}{(- 1) - (- 1)}

\Rightarrow \frac{α}{1} = \frac{β}{1} = \frac{γ}{0} \Rightarrow γ = 0

it is given that

α + γ = 1 \Rightarrow α = 1

, so

β = 1

.

And, the mid-point of AB, M(2, 1,

-

1) lies on the given plane, so

2 α + β - γ = δ

\Rightarrow 2 (1) + (1) - 0 = δ \Rightarrow δ = 3

∴

α + β = 2

,

δ - γ = 0

,

δ + β = 4

.

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