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Question: In a triangle ABC, if \(2\overset{\rightarrow}{AC} = 3\overset{\rightarrow}{CB},\) then \(2\overset{...

In a triangle ABC, if 2AC→=3CB→,2\overset{\rightarrow}{AC} = 3\overset{\rightarrow}{CB}, then 2OA→+3OB→2\overset{\rightarrow}{OA} + 3\overset{\rightarrow}{OB} equals

A

5OC→5\overset{\rightarrow}{OC}

B

13(2i−2j+k)\frac{1}{3}(2\mathbf{i} - 2\mathbf{j} + \mathbf{k})

C

OC→\overset{\rightarrow}{OC}

D

None of these

Answer

5OC→5\overset{\rightarrow}{OC}

Explanation

Solution

2OA→+3OB→=2(OC→+CA→)+3(OC→+CB→)2\overset{\rightarrow}{OA} + 3\overset{\rightarrow}{OB} = 2(\overset{\rightarrow}{OC} + \overset{\rightarrow}{CA}) + 3(\overset{\rightarrow}{OC} + \overset{\rightarrow}{CB})

=5OC→+2CA→+3CB→=5OC→= 5\overset{\rightarrow}{OC} + 2\overset{\rightarrow}{CA} + 3\overset{\rightarrow}{CB} = 5\overset{\rightarrow}{OC}, {∵2CA→=−3CB→}\{\because 2\overset{\rightarrow}{CA} = - 3\overset{\rightarrow}{CB}\}.