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Vector Algebra

Question
CBSEENMA12034091
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 space if two vectors straight a with rightwards arrow on top space and space straight b with rightwards arrow on top are such that 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 3 space and space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 4.

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 3 comma space space space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 4
Now,  open vertical bar straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top close vertical bar squared space equals space left parenthesis straight a with rightwards arrow on top minus 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 straight a with rightwards arrow on top. space straight a with rightwards arrow on top space minus space straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top space minus space straight b with rightwards arrow on top. space straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top. space straight b with rightwards arrow on top
equals space open vertical bar straight a with rightwards arrow on top close vertical bar squared space minus space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space minus space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space plus space open vertical bar straight b with rightwards arrow on top close vertical bar squared equals space left parenthesis 2 right parenthesis squared minus 4 minus 4 plus left parenthesis 3 right parenthesis squared 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 space equals space 4 minus space 4 minus 4 plus 9 space equals space 5 therefore space space space space space space open vertical bar straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top close vertical bar space equals space square root of 5

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