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Question: The points with position vectors \(10\mathbf{i} + 3\mathbf{j},12\mathbf{i} - 5\mathbf{j}\) and \(a\m...

The points with position vectors 10i+3j,12i−5j10\mathbf{i} + 3\mathbf{j},12\mathbf{i} - 5\mathbf{j} and ai+11ja\mathbf{i} + 11\mathbf{j} are collinear, if a=a =

A

– 8

B

4

C

8

D

12

Answer

8

Explanation

Solution

If given points be A,B,CA,B,C then AB→=k(BC→)\overset{\rightarrow}{AB} = k(\overset{\rightarrow}{BC}) or 2i−8j=k[(a−12)i+16j]⇒k=−122\mathbf{i} - 8\mathbf{j} = k\lbrack(a - 12)\mathbf{i} + 16\mathbf{j}\rbrack \Rightarrow k = \frac{- 1}{2}

Also, 2=k(a−12)⇒a=8.2 = k(a - 12) \Rightarrow a = 8.