If the image of the point $(4,4,3)$ in the line $\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-1}{3}$ is $(\alpha, \beta, \gamma)$, then $\alpha+\beta+\gamma$ is equal to

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Aicharya · Accepted Answer

Let coordinate of $R=(2 r+1, r+2,3 r+1)$
$\because \quad P R$ is perpendicular to given line.
$\therefore(2 r-3) \cdot 2+(r-2) \cdot 1+(3 r-2) \cdot 3=0$
$\therefore r=1$
$\therefore$ Coordinate of $R=(3,3,4)$
$\therefore \quad(\alpha, \beta, \gamma)=(2,2,5)$
$\therefore \alpha+\beta+\gamma=9$ ^

If the image of the point $(4,4,3)$ in the line $\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-1}{3}$ is $(\alpha,…

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