Answer :

Given -


A = (2,5,1)


B = (1,2,-1)


C = (3,λ,3)


To find – The value of λ so that A, B and C are collinear


Formula to be used – If P = (a,b,c) and Q = (a’,b’,c’),then the direction ratios of the line PQ is given by ((a’-a),(b’-b),(c’-c))


The direction ratios of the line AB can be given by


((1-2),(2-5),(-1-1))


=(-1,-3,-2)


Similarly, the direction ratios of the line BC can be given by


((3-1),(λ-2),(3+1))


=(2,λ-2,4)


Tip – If it is shown that direction ratios of AB=α times that of BC , where λ is any arbitrary constant, then the condition is sufficient to conclude that points A, B and C will be collinear.


So, d.r. of AB


=(-1,-3,-2)


=(-1/2)Χ(2,λ-2,4)


=(-1/2)Хd.r. of BC


Since, A, B and C are collinear,





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