A) \[(2,3)\]
B) \[(3,4)\]
C) \[(4,5)\]
D) \[(1,2)\]
Correct Answer: B
Solution :
| Let the foot of perpendicular from \[P(2,-1,4)\] to the given line be\[A(10\lambda -3,-7\lambda +2,\lambda )\] |
| \[\overrightarrow{PA.}(10i-7j+k)=0\]\[\Rightarrow \]\[10(10\lambda -5)-7(-7\lambda +3)+1(\lambda -4)=0\]\[\Rightarrow \]\[150\lambda =75\]\[\Rightarrow \]\[\lambda =\frac{1}{2}\] |
| \[|\overrightarrow{PA}|=\sqrt{{{(10\lambda -5)}^{2}}+{{(-7\lambda +3)}^{2}}+{{(\lambda -4)}^{2}}}\] |
| \[=\sqrt{0+{{\left( \frac{1}{2} \right)}^{2}}+{{\left( \frac{7}{2} \right)}^{2}}}=\sqrt{\frac{50}{4}}\] |
| Which lies in\[(3,4).\] |
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