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 \[PL\,\,\left\langle 2\lambda ,\,\,-3\lambda -1,\,\,8\lambda -10 \right\rangle \] |
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 mid 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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