# If the points wit

Let us understand that, two more points are said to be collinear if they all lie on a single straight line.

Let the points be A, B and C having position vectors such that,   So, let us find and .

Therefore, is given by    …(i)

And is given by    …(ii)

Since, it has been given that points A, B and C are collinear.

So, we can write as Where λ = a scalar quantity

Put the values of and from (i) and (ii), we get  Comparing the vectors and respectively, we get

a – 12 = 2λ …(iii)

and, 16 = –8λ

From –8λ = 16, we can find the value of λ.

–8λ = 16 λ = –2

Put λ = –2 in equation (iii), we get

a – 12 = 2λ

a – 12 = 2(–2)

a – 12 = –4

a = –4 + 12

a = 8

Thus, we have got a = 8.

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