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let (\alpha ,\beta ,\gamma ) be the image of the point P (2, 3, 5) in the plane2x+y-3z=6 then \alpha +\beta +\gamma is equal to

Option: 1

5


Option: 2

9


Option: 3

10


Option: 4

12


Answers (1)

best_answer

\begin{array}{llc} \frac{\alpha-2}{2}=\frac{\beta-3}{1}=\frac{\gamma-5}{-3}=-2\left(\frac{2 \times 2+3-3 \times 5-6}{2^2+1^2+1-3^2}\right)=2 \\ \frac{\alpha-2}{2}=2 & \beta-3=2 & \gamma-5=-6 \\ \alpha=6 & \beta=5 & \gamma=-1 \end{array}

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