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  • Let the image of the point in the plane <img alt="2 x-y+z=9" src="https://entrancecorner.oncodecogs.com/

Let the image of the point P(1,2,3)in the plane 2 x-y+z=9 be Q.If the coordinates of the point R are (6, 10,7) . then the square of the area of the triangle PQR is ____.

Option: 1

594


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

Let \mathrm{Q}(\alpha, \beta, \gamma)  be the image of \mathrm{P}, about the plane

2 \mathrm{x}-\mathrm{y}+\mathrm{z}=9
\frac{\alpha-1}{2}=\frac{\beta-2}{-1}=\frac{\gamma-3}{1}=2
\Rightarrow \alpha=5, \beta=0, \gamma=5
\text{Then area of triangle }\mathrm{PQR} is =\frac{1}{2}|\overrightarrow{\mathrm{PQ}} \times \overrightarrow{\mathrm{PR}}|
=|-12 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}+21 \hat{\mathrm{k}}|=\sqrt{144+9+441}=\sqrt{594}

Square of area =594

Posted by

sudhir.kumar

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