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Vector Algebra

Question
CBSEENMA12034080
Wired Faculty App

Find open vertical bar straight a with rightwards arrow on top close vertical bar and open vertical bar straight b with rightwards arrow on top close vertical bar comma if  open parentheses straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top close parentheses. space left parenthesis straight a with rightwards arrow on top space minus straight b with rightwards arrow on top right parenthesis space equals space 12 space and space open vertical bar straight a with rightwards arrow on top close vertical bar space equals 2 space open vertical bar straight b with rightwards arrow on top close vertical bar.

Solution

We have
        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 minus straight b with rightwards arrow on top right parenthesis space equals space 12
therefore space 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 space 12 rightwards double arrow space space space space left parenthesis 2 space open vertical bar straight b with rightwards arrow on top close vertical bar right parenthesis squared space minus space open vertical bar straight b with rightwards arrow on top close vertical bar squared space equals space 12 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets because space open vertical bar straight a with rightwards arrow on top close vertical bar space equals space 2 space open vertical bar straight b with rightwards arrow on top close vertical bar close square brackets rightwards double arrow space space space space 4 space open vertical bar straight b with rightwards arrow on top close vertical bar squared space minus open vertical bar straight b with rightwards arrow on top close vertical bar squared space equals 12 space space space space space space space space rightwards double arrow space space 3 space open vertical bar straight b with rightwards arrow on top close vertical bar squared space equals space 12 therefore space space space space open vertical bar straight b with rightwards arrow on top close vertical bar squared space equals space 4 space space space space space space space 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 space space equals space 2 therefore space space space space open vertical bar straight a with rightwards arrow on top close vertical bar space equals space 2 space cross times 2 space equals space 4 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets because space space open vertical bar straight a with rightwards arrow on top close vertical bar space equals space 2 space open vertical bar straight b with rightwards arrow on top close vertical bar close square brackets space space

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