Determine the values of a and b so that the points (a,b,3),(2,0,-1) and (1,-1,-3) are collinear.
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Solution
If the three points A, B and C are collinear, then the direction ration of AB is proportional to that of BC is proportional to that of CA A(a,b,3) B(2,0,-1) C(1,-1,3) Direction ratio of AB =(2-a,-b,-1-3) =(2-a,-b,-4) Direction ratio of BC =(1-2,-1,3+1) = (-1,-1,4) Direction ratio of AC =(1-a,-1-b,3-3) = (1-a,-1-b,0)
Now we have 2-a/-1=-b/-1=-4/4 -2+a=-1 a=-1+2 a=1 b=-1 We would get the same answer for a and b on comparing direction ratios of AC and DC