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Vector Algebra

Question
CBSEENMA12033947
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Give a condition that the three vectors straight a with rightwards arrow on top comma space straight b with rightwards arrow on top space and space straight c with rightwards arrow on top form the three sides of a triangle. What are the other possibilities?

Solution

Let OA with rightwards arrow on top space equals space straight a with rightwards arrow on top comma space space AB with rightwards arrow on top space equals space straight b with rightwards arrow on top comma space space space BO with rightwards arrow on top space equals space straight c with rightwards arrow on top
Now,     OA with rightwards arrow on top space plus space AB with rightwards arrow on top space equals space OB with rightwards arrow on top
therefore space space space space space space space straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top space equals space minus straight c with rightwards arrow on top therefore space space space space space straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top space plus space straight c with rightwards arrow on top space equals space 0 with rightwards arrow on top
Other possibilities are
                 straight a with rightwards arrow on top space equals space straight b with rightwards arrow on top plus straight c with rightwards arrow on top comma space
                 straight b with rightwards arrow on top space equals space straight c with rightwards arrow on top space plus space straight a with rightwards arrow on top comma space space space straight c 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

Other possibilities are
                    straight a with rightwards arrow on top space equals space straight b with rightwards arrow on top space plus space straight c with rightwards arrow on top comma straight b with rightwards arrow on top space equals space straight c with rightwards arrow on top space plus space straight a with rightwards arrow on top comma space space straight c 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

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