A) (-3, 2, 1)
B) (1, 2, 2)
C) (4, 5, 3)
D) none of these
Correct Answer: D
Solution :
[d] Let AD be the perpendicular and D be the foot of the perpendicular which divides BC in the ratio \[\lambda :1\], then \[D\left( \frac{10\lambda -9}{\lambda +1},\frac{4}{\lambda +1},\frac{-\lambda +5}{\lambda +1} \right)\]. ...(i) The direction ratios of AD are \[\frac{10\lambda -9}{\lambda +1},\frac{4}{\lambda +1}\]and \[\frac{-\lambda +5}{\lambda +1}\] and direction ratios of BC are 19, \[-\]4 and \[-\]6. Since \[AD\bot BC,\]we get \[19\left( \frac{10\lambda -9}{\lambda +1} \right)-4\left( \frac{4}{\lambda +1} \right)-6\left( \frac{-\lambda +5}{\lambda +1} \right)=0\] Or \[\lambda =\frac{31}{28}\] Hence, on putting the value of \[\lambda \] in (i), we get required foot of the perpendicular, i.e., \[\left( \frac{58}{59},\frac{112}{59},\frac{109}{59} \right)\]You need to login to perform this action.
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