In a triangle ABC , if 2AC = 3CB , then 2OA + 3OB equals - Vidyadip

MCQ

In a triangle $ ABC$ , if $2\overrightarrow {AC} = 3\overrightarrow {CB} ,$ then $2\overrightarrow {OA} + 3\overrightarrow {OB} $ equals

✓
$5\overrightarrow {OC} $
B
$-\overrightarrow {OC} $
C
$\,\overrightarrow {OC} $
D
None of these

✓

Answer

Correct option: A.

$5\overrightarrow {OC} $

a
(a) $2\overrightarrow {OA} + 3\overrightarrow {OB} = 2(\overrightarrow {OC} + \overrightarrow {CA} ) + 3\,(\overrightarrow {OC} + \overrightarrow {CB} )$

$ = 5\overrightarrow {OC} + 2\overrightarrow {CA} + 3\overrightarrow {CB} = 5\overrightarrow {OC} $, .$\{ \because \,2\overrightarrow {CA} = - 3\overrightarrow {CB} \} $

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