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Vector Algebra

Question
CBSEENMA12034084
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If straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space straight a with rightwards arrow on top. space straight c with rightwards arrow on top comma spaceprove that either straight a with rightwards arrow on top space equals space 0 with rightwards arrow on top or straight b with rightwards arrow on top space equals space straight c with rightwards arrow on top  or  straight a with rightwards arrow on top  is perpendicular to straight b with rightwards arrow on top minus straight c with rightwards arrow on top.

Solution
because space space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space straight a with rightwards arrow on top. space straight c with rightwards arrow on top. space space space space space rightwards double arrow space space space space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space minus space straight a with rightwards arrow on top. space straight c with rightwards arrow on top space equals space 0 therefore space space space straight a with rightwards arrow on top. space left parenthesis straight b with rightwards arrow on top minus straight c with rightwards arrow on top right parenthesis space equals 0 with rightwards arrow on top comma space space space space rightwards double arrow space space space space space space straight a with rightwards arrow on top space equals space 0 with rightwards arrow on top comma space space straight b with rightwards arrow on top space minus space straight c with rightwards arrow on top space equals 0 with rightwards arrow on top space or space space straight a with rightwards arrow on top space is space perp. space to space straight b with rightwards arrow on top minus straight c with rightwards arrow on top rightwards double arrow space space straight a with rightwards arrow on top space equals space 0 with rightwards arrow on top comma space space space straight b with rightwards arrow on top space equals space straight c with rightwards arrow on top space or space space straight a with rightwards arrow on top space space is space perpendicular space to space straight b with rightwards arrow on top minus straight c with rightwards arrow on top.

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