Let be the mirror image of ( 1 , - 2 , 3 ) in the line x + 1 2 = y - 3 4 = z + 2 3 then 2 + 4 + 3 + 2 =

Question

Let $(α, β, γ)$ be the mirror image of $(1, - 2, 3)$ in the line $\frac{x + 1}{2} = \frac{y - 3}{4} = \frac{z + 2}{3}$ then $2 α + 4 β + 3 γ + 2 =____$

Smart Achievers · Accepted Answer

(1)

$A B ⊥ line, (α - 1) 2 + 4 (β + 2) + 3 (γ - 3) = 0$

$∴$ $2 α + 4 β + 3 γ = 3$

Solution

Q.
Let $(α, β, γ)$ be the mirror image of $(1, - 2, 3)$ in the line $\frac{x + 1}{2} = \frac{y - 3}{4} = \frac{z + 2}{3}$ then $2 α + 4 β + 3 γ + 2 =____$

1 5

2 11

3 9

4 10

Ans.
(1)

$A B ⊥ line, (α - 1) 2 + 4 (β + 2) + 3 (γ - 3) = 0$

$∴$ $2 α + 4 β + 3 γ = 3$

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