Q. 45.0( 3 Votes )

If the points wit

Answer :

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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