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JEE Main 2024
05-04-2024 S2
Question
Let $(\alpha, \beta, \gamma)$ be the point $(8,5,7)$ in the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-2}{5}$. Then $\alpha+\beta+\gamma$ is equal to
Select the correct option:
A
16
B
18
C
14
D
20
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution

$\begin{aligned} & \overrightarrow{\mathrm{AM}} \cdot(2 \hat{\imath}+3 \hat{\jmath}+5 \hat{k})=0 \\ & (2 \lambda-7)(2)+(3 \lambda-6)(3)+(5 \lambda-5)(5)=0 \\ & 38 \lambda=57 \\ & \lambda=\frac{3}{2}\end{aligned}$
$\begin{aligned} & \mathrm{M}\left(4, \frac{7}{2}, \frac{19}{2}\right) \\ & \mathrm{A}^{\prime}(0,2,12)\end{aligned}$
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