Answer Given –
A = (3,2,-4)
B = (9,8,-10)
C = (λ,μ,-6)
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 ((9-3),(8-2),(-10+4))
=(6,6,-6)
Similarly, the direction ratios of the line BC can be given by ((λ-9),(μ-8),(-6+10))
=(λ-9,μ-8,4)
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
=(6,6,-6)
=(-6/4)Χ(-4,-4,4)
=(-3/2)Хd.r. of BC
Since, A, B and C are collinear,