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Vector Algebra

Question
CBSEENMA12034136
Wired Faculty App

Three vectors straight a with rightwards arrow on top comma space straight b with rightwards arrow on top space and space straight c with rightwards arrow on top satisfy the condition straight a with rightwards arrow on top plus straight b with rightwards arrow on top plus straight c with rightwards arrow on top space equals 0 with rightwards arrow on top. Evaluate the quantity straight mu space equals space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space plus straight b with rightwards arrow on top. space straight c with rightwards arrow on top space plus space straight c with rightwards arrow on top. space straight a with rightwards arrow on top comma space if space open vertical bar straight a with rightwards arrow on top close vertical bar space equals 1 comma space space open vertical bar straight b with rightwards arrow on top close vertical bar space equals space 4 space and space open vertical bar straight c with rightwards arrow on top close vertical bar space equals space 2.

Solution

Here
        straight a with rightwards arrow on top plus straight b with rightwards arrow on top plus straight c with rightwards arrow on top space equals space 0 with rightwards arrow on top
therefore space space space space space straight a with rightwards arrow on top plus straight b with rightwards arrow on top space equals space minus straight c with rightwards arrow on top                                                       ...(1)
therefore space space space straight a with rightwards arrow on top. space left parenthesis straight a with rightwards arrow on top plus straight b with rightwards arrow on top right parenthesis space equals space minus straight a with rightwards arrow on top. space straight c with rightwards arrow on top rightwards double arrow space space space space space straight a with rightwards arrow on top. space straight a with rightwards arrow on top space plus space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space minus straight a with rightwards arrow on top. space straight c with rightwards arrow on top rightwards double arrow space space space space open vertical bar straight a with rightwards arrow on top close vertical bar squared plus space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space plus space straight a with rightwards arrow on top. space straight c with rightwards arrow on top space equals space 0 therefore space space space space 1 plus straight a with rightwards arrow on top. space straight b with rightwards arrow on top space plus space straight a with rightwards arrow on top. space straight c with rightwards arrow on top space equals 0 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 1 close square brackets therefore space space space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space plus space straight a with rightwards arrow on top. space straight c with rightwards arrow on top space equals space minus 1 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... left parenthesis 2 right parenthesis From space left parenthesis 1 right parenthesis comma space space straight b with rightwards arrow on top. space left parenthesis straight a with rightwards arrow on top plus straight b with rightwards arrow on top right parenthesis equals space minus straight b with rightwards arrow on top. space straight c with rightwards arrow on top space space space rightwards double arrow space space space space straight b with rightwards arrow on top. space straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top. space straight b with rightwards arrow on top space equals space minus straight b with rightwards arrow on top. space straight c with rightwards arrow on top rightwards double arrow space space space space straight b with rightwards arrow on top. space straight a with rightwards arrow on top space plus space open vertical bar straight b with rightwards arrow on top close vertical bar squared space plus space straight b with rightwards arrow on top. space straight c with rightwards arrow on top space equals space 0 rightwards double arrow space space space space space straight b with rightwards arrow on top. space straight a with rightwards arrow on top space plus space 16 space plus space straight b with rightwards arrow on top. space straight c with rightwards arrow on top space equals space 0 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 b with rightwards arrow on top close vertical bar space equals space 4 close square brackets therefore space space space straight b with rightwards arrow on top. space straight a with rightwards arrow on top space plus straight b with rightwards arrow on top. space straight c with rightwards arrow on top space equals space minus 16 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... left parenthesis 3 right parenthesis space space space space space space Again space from space left parenthesis 1 right parenthesis comma space straight c with rightwards arrow on top. space left parenthesis straight a with rightwards arrow on top plus straight b with rightwards arrow on top right parenthesis space equals space minus straight c with rightwards arrow on top. space straight c with rightwards arrow on top therefore space space straight c with rightwards arrow on top. space straight a with rightwards arrow on top space plus space straight c with rightwards arrow on top. space straight b with rightwards arrow on top space equals space minus space open vertical bar straight c with rightwards arrow on top close vertical bar squared rightwards double arrow space space straight c with rightwards arrow on top. straight a with rightwards arrow on top space plus space straight c with rightwards arrow on top. space straight b with rightwards arrow on top space equals space minus 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 space space space... left parenthesis 4 right parenthesis
                                                                                   open square brackets because space space open vertical bar straight c with rightwards arrow on top close vertical bar space equals space 2 close square brackets
Adding (2), (3) and (4), we get
                   2 left parenthesis straight a with rightwards arrow on top. space straight b with rightwards arrow on top space plus space straight b with rightwards arrow on top. space straight c with rightwards arrow on top space plus space straight c with rightwards arrow on top. space straight a with rightwards arrow on top right parenthesis space equals space minus 21 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 straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space straight b with rightwards arrow on top. space straight a with rightwards arrow on top space etc close square brackets therefore space space space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space plus space straight b with rightwards arrow on top. space straight c with rightwards arrow on top space plus space straight c with rightwards arrow on top. space straight a with rightwards arrow on top space equals space minus 21 over 2 rightwards double arrow space space space space space space space space space space straight mu space equals space minus 21 over 2

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