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Vector Algebra

Question
CBSEENMA12034092
Wired Faculty App

Find open vertical bar straight a with rightwards arrow on top minus straight b with rightwards arrow on top close vertical bar comma if open vertical bar straight a with rightwards arrow on top close vertical bar space equals space 2 comma space space space open vertical bar straight b with rightwards arrow on top close vertical bar space equals space 5 space space and space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 8

Solution

Here open vertical bar straight a with rightwards arrow on top close vertical bar space equals space 2 comma space space open vertical bar straight b with rightwards arrow on top close vertical bar space equals space 5 comma space space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 8                       ...(1)
Now,    open vertical bar straight a with rightwards arrow on top minus straight b with rightwards arrow on top close vertical bar squared space equals space left parenthesis straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top right parenthesis squared space equals straight a with rightwards arrow on top squared plus straight b with rightwards arrow on top squared space minus space 2 space straight a with rightwards arrow on top. straight b with rightwards arrow on top space equals space open vertical bar straight a with rightwards arrow on top close vertical bar squared plus space open vertical bar straight b with rightwards arrow on top close vertical bar squared space minus space 2 space straight a with rightwards arrow on top. space straight b with rightwards arrow on top
                          equals 4 plus 25 minus 16                                    open square brackets because space of space left parenthesis 1 right parenthesis close square brackets
                           equals space 13
therefore space space space open vertical bar straight a with rightwards arrow on top space minus straight b with rightwards arrow on top close vertical bar space equals space square root of 13

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