A) \[(3,\,5,-2)\]
B) \[(-3,\,5,2)\]
C) \[(3,-5,2)\]
D) \[(-1,\,4,2)\]
Correct Answer: B
Solution :
The image of the point \[({{x}_{1}},{{y}_{1}},{{z}_{1}})\] in the plane \[ax+by+cz+d=0\]is \[\frac{x-{{x}_{1}}}{a}=\frac{y-{{y}_{1}}}{b}=\frac{z-{{z}_{1}}}{c}\] \[=\frac{-2(a{{x}_{1}}+b{{y}_{1}}+c{{z}_{1}}+d)}{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}\] \[\therefore \]\[\frac{x-1}{2}=\frac{y-3}{-1}=\frac{z-4}{1}=-2\left( \frac{2-3+4+3}{6} \right)\] \[\Rightarrow \] \[z=-3,\,y=5\] and \[z=2\] \[\therefore \] image of the point is \[(-3,5,2)\].
You need to login to perform this action.
You will be redirected in
3 sec
