A) (1, 2, 7)
B) (1, ?2, 7)
C) (?1, 2, 7)
D) (1, ?2, ?7)
Correct Answer: B
Solution :
Ratio \[-\left[ \frac{2\,\,(2)+(-\,3)(1)+(1)(1)-7}{2\,\,(3)+(-\,4)(1)+(-\,5)(1)-7} \right]=-\,\,\left[ \frac{-\,5}{-\,10} \right]=-\,\,\left( \frac{1}{2} \right)\] \[\therefore \,\,\,x=\frac{2\,(2)-\,3\,(1)}{1}=1,\,\,y=\frac{-\,3\,(2)\,-\,(\,-\,4)}{1}=-2\] and \[z=\frac{1\,(2)\,-\,(-\,5)}{1}=7\]. Therefore, \[P\,(1,\,-\,2,\,\,7)\]. Trick : As (1, ? 2, 7) and (? 1, 2, 7) satisfy the equation \[2x+y+z=7,\] but the point (1, ? 2, 7) is collinear with (2, ? 3, 1) and (3, ? 4, ? 5). Note : If a point dividing the join of two points in some particular ratio, then this point must be collinear with the given points.
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