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Vector Algebra

Question
CBSEENMA12034057
Wired Faculty App

If straight a with rightwards arrow on top is the unit vector and open parentheses straight x with rightwards arrow on top minus straight a with rightwards arrow on top close parentheses. space left parenthesis straight x with rightwards arrow on top space plus space straight a with rightwards arrow on top right parenthesis space equals space 8 comma then find open vertical bar straight x with rightwards arrow on top close vertical bar.

Solution

Since straight a with rightwards arrow on top is a unit vector
                     open vertical bar straight a with rightwards arrow on top close vertical bar space equals space 1                                               ...(1)
Now,    left parenthesis straight x with rightwards arrow on top minus straight a with rightwards arrow on top right parenthesis. space left parenthesis straight x with rightwards arrow on top plus straight a with rightwards arrow on top right parenthesis space equals space 8 space space space space rightwards double arrow space space space straight x with rightwards arrow on top. space straight x with rightwards arrow on top space plus space straight x with rightwards arrow on top. space straight a with rightwards arrow on top space minus space straight a with rightwards arrow on top. space straight x with rightwards arrow on top space minus space straight a with rightwards arrow on top. space straight a with rightwards arrow on top space equals space 8
therefore space space open vertical bar straight x with rightwards arrow on top close vertical bar squared plus space straight x with rightwards arrow on top. space straight a with rightwards arrow on top space minus space straight x with rightwards arrow on top. space straight a with rightwards arrow on top space minus space open vertical bar straight a with rightwards arrow on top close vertical bar squared space equals space 8 space space space space space space space space space space space space space space space space space space space left square bracket because space space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals straight b with rightwards arrow on top. space straight a with rightwards arrow on top right square bracket therefore space space space open vertical bar straight x with rightwards arrow on top close vertical bar squared space minus space left parenthesis 1 right parenthesis squared space equals 8 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 space space space space space space space open square brackets because space of space left parenthesis 1 right parenthesis close square brackets rightwards double arrow space space space space open vertical bar straight x with rightwards arrow on top close vertical bar squared space equals space 9 space space space space space space space space space rightwards double arrow space space space space space open vertical bar straight x with rightwards arrow on top close vertical bar space equals space 3

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