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Vector Algebra

Question
CBSEENMA12033944
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straight a with rightwards arrow on top space and space straight b with rightwards arrow on top are two non-collinear vectors having the same initial point. What vectorn is represented by straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top?

Solution

Let   OA with rightwards arrow on top space equals space straight a with rightwards arrow on top comma space space space OB with rightwards arrow on top space equals space straight b with rightwards arrow on top
therefore space space space space space space AC with rightwards arrow on top space equals space OB with rightwards arrow on top space equals space straight b with rightwards arrow on top
Now,   OC with rightwards arrow on top space equals space OA with rightwards arrow on top space plus space AC with rightwards arrow on top
 therefore space space space space OC with rightwards arrow on top space equals space straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top
therefore space space space space straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top is the vector represented by the diagonal OC.

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