Answer :

Given -


A = (2,3,-4)


B = (1,-2,3)


C = (3,8,-11)


To prove – 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),(-2-3),(3+4))


=(-1,-5,7)


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


((3-1),(8+2),(-11-3))


=(2,10,-14)


Tip – If it is shown that direction ratios of AB=λ 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,-5,7)


=(-1/2)Χ(2,10,-14)


=(-1/2)Хd.r. of BC


Hence, A, B and C are collinear


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