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Vector Algebra

Question
CBSEENMA12033954
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If AO with rightwards arrow on top space plus space OB with rightwards arrow on top space equals space BO with rightwards arrow on top space plus space OC with rightwards arrow on top comma space then prove that the points A, B and C are collinear.

Solution

We have AO with rightwards arrow on top space plus space OB with rightwards arrow on top space equals space BO with rightwards arrow on top space plus space OC with rightwards arrow on top
therefore space space space space space space space space AB with rightwards arrow on top space equals space BC with rightwards arrow on top
( Triangle Law of Vectors)
therefore space space space space space AB with rightwards arrow on top space and space BC with rightwards arrow on top space are parallel vectors. 
But B is the common point . 
therefore space space space space space AB with rightwards arrow on top space and space BC with rightwards arrow on top are along the same line
∴ point A, B and C are collinear.

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