A) \[(3,-\,4,-\,2)\]
B) \[(5,-\,8,-\,4)\]
C) \[(1,-\,1,-\,10)\]
D) \[(2,-3,\,8)\]
Correct Answer: B
Solution :
\[\frac{x-1}{2}=\frac{y+1}{-3}=\frac{z+10}{8}=\lambda \] |
\[L(2\lambda +1,\,\,-3\lambda -1,\,\,8\lambda -10)\] |
Direction ratio of \[PL\,\,(2\lambda ,\,\,-3\lambda -1,\,\,8\lambda -10)\] |
PL and AB are perpendicular lines |
\[2\,\,(2\lambda )-3\,\,(-\,3\,\lambda +1)+8\,\,(8\,\lambda -10)=0\]\[\Rightarrow 77\lambda -77=0\]\[\Rightarrow \lambda =1\] |
\[L(3,-\,4,-\,2)\] |
L is the mind point of PQ |
\[Q\,({{x}_{1}},{{y}_{1}},{{z}_{1}})\] |
Then |
\[\frac{{{x}_{1}}+1}{2}=3\]\[\Rightarrow {{x}_{1}}=5\] |
\[\frac{{{y}_{1}}+0}{2}=-\,4\] |
\[\Rightarrow {{y}_{1}}=-\,8\] and \[\frac{{{z}_{1}}+0}{2}=-2\]\[\Rightarrow {{z}_{1}}=-\,4\] |
reflection point of P is \[(5,-\,8,-\,4)\] |
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