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  • Let P be the plane passing through the line <img alt="\frac{x-1}{1}=\frac{y-2}{-3}=\frac{z+5}{7}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cfrac%7Bx-1%7D%7B1%7D%3D%5Cfrac%7By-2%7

Let P be the plane passing through the line \frac{x-1}{1}=\frac{y-2}{-3}=\frac{z+5}{7} and the point (2,4,-3) 

If the image of the  then  point (-1, 3, 4) in the plane P is (\alpha ,\beta ,\gamma ) then \alpha +\beta +\gamma is equal to

Option: 1

12


Option: 2

9


Option: 3

10


Option: 4

11


Answers (1)

best_answer

Equation of plane is given by\begin{aligned} & \left|\begin{array}{ccc} x-1 & y-2 & z+5 \\ 1 & 2 & 2 \\ 1 & -3 & 7 \end{array}\right|=0 \\ & 4 x-y-z=7 \\ & \frac{\alpha+1}{4}=\frac{\beta-3}{-1}=\frac{\gamma-4}{-1}=\frac{-2(-4-3-4-7)}{16+1+1}=2 \\ & \alpha=7, \beta=1, \gamma=2 \\ & \alpha+\beta+\gamma=10(\text { Option } 3) \end{aligned}

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vishal kumar

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