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Vector Algebra

Question
CBSEENMA12034250
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If 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  are mutually perpendicular unit vectors and straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top space equals space straight c with rightwards arrow on top comma then straight b with rightwards arrow on top space equals straight c with rightwards arrow on top space cross times straight a with rightwards arrow on top space and space straight a with rightwards arrow on top space equals space straight b with rightwards arrow on top space cross times space straight c with rightwards arrow on top.

Solution

Since,  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 are mutually perpendicular  unit vectors
therefore space space space space space space open vertical bar straight a with rightwards arrow on top close vertical bar space equals space 1 comma space space space open vertical bar straight b with rightwards arrow on top close vertical bar space equals space open vertical bar straight c with rightwards arrow on top close vertical bar space equals space 1 and space space space space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space straight b with rightwards arrow on top. space straight c with rightwards arrow on top space equals space straight c with rightwards arrow on top. space straight a with rightwards arrow on top space equals space 0 Also comma space space space space straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top space equals space straight c with rightwards arrow on top therefore space space space space straight c with rightwards arrow on top space is space perpendicular space to space the space plane space of space straight a with rightwards arrow on top space and space straight b with rightwards arrow on top therefore space space space space straight b with rightwards arrow on top space is space perpendicular space to space the space plane space of space straight c with rightwards arrow on top space and space straight a with rightwards arrow on top comma space space space space space space space space space straight a with rightwards arrow on top space is space perpendicular space to space the space plane space straight b with rightwards arrow on top space and space straight c with rightwards arrow on top therefore space space straight b with rightwards arrow on top space equals space straight c with rightwards arrow on top space cross times space straight a with rightwards arrow on top space. space straight a with rightwards arrow on top space equals space straight b with rightwards arrow on top space cross times space straight c with rightwards arrow on top.

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