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Vector Algebra

Question
CBSEENMA12034081
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Find open vertical bar straight a with rightwards arrow on top close vertical bar space and space space open vertical bar straight b with rightwards arrow on top close vertical bar space if space left parenthesis straight a with rightwards arrow on top plus straight b with rightwards arrow on top right parenthesis. space left parenthesis straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top right parenthesis space equals space 8 space space and space open vertical bar straight a with rightwards arrow on top close vertical bar space equals space 8 space open vertical bar straight b with rightwards arrow on top close vertical bar.

Solution

  left parenthesis straight a with rightwards arrow on top plus straight b with rightwards arrow on top right parenthesis. space left parenthesis straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top right parenthesis space equals space 8 space space space space rightwards double arrow space space space open vertical bar straight a with rightwards arrow on top close vertical bar squared minus space open vertical bar straight b with rightwards arrow on top close vertical bar squared space equals 8
rightwards double arrow space space 64 space open vertical bar straight b with rightwards arrow on top close vertical bar squared space minus space open vertical bar straight b with rightwards arrow on top close vertical bar squared space equals space 8                                                        open square brackets because space space space open vertical bar straight a with rightwards arrow on top close vertical bar space equals space 8 space open vertical bar straight b with rightwards arrow on top close vertical bar close square brackets
rightwards double arrow space space space space 63 space open vertical bar straight b with rightwards arrow on top close vertical bar squared space equals space 8 space space space space space space space space space space rightwards double arrow space space space space open vertical bar straight b with rightwards arrow on top close vertical bar squared space equals space 8 over 63 space space space space space space space rightwards double arrow open vertical bar straight b with rightwards arrow on top close vertical bar space equals fraction numerator 2 square root of 2 over denominator square root of 63 end fraction therefore space space space space space space space space open vertical bar straight a with rightwards arrow on top close vertical bar space equals 8 space cross times space fraction numerator 2 space square root of 2 over denominator square root of 63 end fraction space equals fraction numerator 16 space square root of 2 over denominator square root of 63 end fraction

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