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Vector Algebra

Question
CBSEENMA12033953
Wired Faculty App

If straight a with rightwards arrow on top comma space straight b with rightwards arrow on top comma space straight c with rightwards arrow on top be the vectors represented by the sides of a triangle, taken in order, then prove that 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.

Solution

Let ABC be a triangle such that 
           BC with rightwards arrow on top space equals space straight a with rightwards arrow on top. space space CA with rightwards arrow on top space equals space straight b with rightwards arrow on top space. space AB with rightwards arrow on top space equals space straight c with rightwards arrow on top
L.H.S. = 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
           equals space BC with rightwards arrow on top space plus space CA with rightwards arrow on top space plus space AB with rightwards arrow on top space equals space open parentheses BC with rightwards arrow on top space plus space CA with rightwards arrow on top close parentheses space plus space AB with rightwards arrow on top
             equals space BA with rightwards arrow on top space plus space AB with rightwards arrow on top

                                                            open square brackets because space space space BC with rightwards arrow on top space plus space CA with rightwards arrow on top space equals AB with rightwards arrow on top space by space triangle space law space of space addition close square brackets
                 equals space AB with rightwards arrow on top space plus space AB with rightwards arrow on top space space equals space 0 with rightwards arrow on top space equals space straight R. straight H. straight S. therefore 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 space equals space 0 with rightwards arrow on top. space
             

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