Answer Given –
A = (-1,4,-2) B = (λ,μ,1)
C = (0,2,-1)
To find – The value of λ and μ 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 ((λ+1),(μ-4),(1+2))
=(λ+1,μ-4,3)
Similarly, the direction ratios of the line BC can be given by ((0-λ),(2-μ),(-1-1))
=(-λ,2-μ,-2)
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
=(λ+1,μ-4,3)
Say, α be an arbitrary constant such that d.r. of AB = α Х d.r. of BC So, 3 = α Х (-2)
i.e. α = -3/2
Since, A, B and C are collinear,