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Question: If **a** and **b** are the position vectors of A and B respectively, then the position vector of a p...

If a and b are the position vectors of A and B respectively, then the position vector of a point C on AB produced such that AC→=3AB→\overset{\rightarrow}{AC} = 3\overset{\rightarrow}{AB} is

A

3a−b3\mathbf{a} - \mathbf{b}

B

3b−a3\mathbf{b} - \mathbf{a}

C

3a−2b3\mathbf{a} - 2\mathbf{b}

D

3b−2a3\mathbf{b} - 2\mathbf{a}

Answer

3b−2a3\mathbf{b} - 2\mathbf{a}

Explanation

Solution

Since given that AC→=3AB→.\overset{\rightarrow}{AC} = 3\overset{\rightarrow}{AB}. It means that point CC divides ABAB externally. Thus AC→:BC→=3:2\overset{\rightarrow}{AC}:\overset{\rightarrow}{BC} = 3:2

Hence OC→=3.b−2.a3−2=3b−2a.\overset{\rightarrow}{OC} = \frac{3.\mathbf{b} - 2.\mathbf{a}}{3 - 2} = 3\mathbf{b} - 2\mathbf{a}.