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Vector Algebra

Question
CBSEENMA12034056
Wired Faculty App

Find open vertical bar straight x with rightwards arrow on top close vertical bar comma space if for a unit vector straight a with rightwards arrow on top comma space 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 12

Solution
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 12
rightwards double arrow space space open vertical bar straight x with rightwards arrow on top close vertical bar squared space minus space open vertical bar straight a with rightwards arrow on top close vertical bar squared space equals space 12 rightwards double arrow 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 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 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 1 close square brackets rightwards double arrow space space open vertical bar straight x with rightwards arrow on top close vertical bar squared space equals space 13 space space space space space space space space space space space space space rightwards double arrow space space space open vertical bar straight x with rightwards arrow on top close vertical bar space equals square root of 13

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