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Vector Algebra

Question
CBSEENMA12034248
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If straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top space equals space straight a with rightwards arrow on top space cross times space straight c with rightwards arrow on top and straight a with rightwards arrow on top not equal to 0 with rightwards arrow on top comma space then straight b with rightwards arrow on top space equals space straight c with rightwards arrow on top space plus space straight lambda space straight alpha with rightwards arrow on top comma space where space straight lambda space is space straight a space scalar.

Solution
straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top space equals space straight a with rightwards arrow on top space cross times space straight c with rightwards arrow on top space space space rightwards double arrow space space space space straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top space minus space straight a with rightwards arrow on top space cross times space straight c with rightwards arrow on top space equals space 0 with rightwards arrow on top
rightwards double arrow space space space straight a with rightwards arrow on top space cross times space left parenthesis straight b with rightwards arrow on top space minus space straight c with rightwards arrow on top right parenthesis space equals space 0 with rightwards arrow on top space space space rightwards double arrow space space space straight b with rightwards arrow on top minus straight c with rightwards arrow on top space is space parallel space to space straight a with rightwards arrow on top rightwards double arrow space space space space straight b with rightwards arrow on top space minus space straight c with rightwards arrow on top space equals space straight lambda space straight a with rightwards arrow on top space space space space space rightwards double arrow space space space straight b with rightwards arrow on top space equals space straight c with rightwards arrow on top space plus space straight lambda space straight a with rightwards arrow on top comma space where space straight lambda space space is space scalar

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