Three Dimensional Geometry Question 22
Question 22 - 2024 (31 Jan Shift 2)
Let $(\alpha, \beta, \gamma)$ be mirror image of the point $(2,3,5)$ in the line $\frac{x-1}{2}-\frac{y-2}{3}-\frac{z-3}{4}$.
Then $2 \alpha+3 \beta+4 \gamma$ is equal to
(1) 32
(2) 33
(3) 31
(4) 34
Show Answer
Answer (2)
Solution
$\because \overrightarrow{\mathrm{PR}} \perp(2,3,4)$
$\therefore \overrightarrow{\mathrm{PR}} \cdot(2,3,4)=0$
$(\alpha-2, \beta-3, \gamma-5) \cdot(2,3,4)=0$
$\Rightarrow 2 \alpha+3 \beta+4 \gamma=4+9+20=33$
