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Vector Algebra

Question
CBSEENMA12033967
Wired Faculty App

If straight c with rightwards arrow on top space equals space 3 straight a with rightwards arrow on top space plus space 4 straight b with rightwards arrow on top and 2 straight c with rightwards arrow on top space equals space straight a with rightwards arrow on top space minus space 3 straight b with rightwards arrow on top, show that
(i) straight c with rightwards arrow on top space and space straight a with rightwards arrow on top have the same direction and open vertical bar straight c with rightwards arrow on top close vertical bar space greater than space open vertical bar straight a with rightwards arrow on top close vertical bar
(ii) straight c with rightwards arrow on top space and space straight b with rightwards arrow on top have opposite direction and 

Solution

Here straight c with rightwards arrow on top space equals space 3 space straight a with rightwards arrow on top space plus space 4 space straight b with rightwards arrow on top and 2 space straight c with rightwards arrow on top space equals space straight a with rightwards arrow on top space minus space 3 space straight b with rightwards arrow on top
therefore space space space 2 space left parenthesis 3 space straight a with rightwards arrow on top space plus space 4 space straight b with rightwards arrow on top right parenthesis space equals space straight a with rightwards arrow on top minus space 3 space straight b with rightwards arrow on top space space space space rightwards double arrow space space space 6 space straight a with rightwards arrow on top space plus space 8 space straight b with rightwards arrow on top space equals space straight a with rightwards arrow on top space minus space 3 space straight b with rightwards arrow on top
rightwards double arrow space space space 5 space straight a with rightwards arrow on top space equals space minus 11 space straight b with rightwards arrow on top therefore space space space space straight a with rightwards arrow on top space equals space minus 11 over 5 straight b with rightwards arrow on top space and space straight b with rightwards arrow on top space equals space minus 5 over 11 straight a with rightwards arrow on top space space space space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis
(i)    straight c with rightwards arrow on top space equals space 3 space straight a with rightwards arrow on top space plus space 4 space straight b with rightwards arrow on top space equals space 3 space straight a with rightwards arrow on top space plus space 4 space open parentheses negative 5 over 11 straight a with rightwards arrow on top close parentheses                             open square brackets because space space of space left parenthesis 1 right parenthesis close square brackets
           equals space 3 space straight a with rightwards arrow on top space minus space 20 over 11 space straight a with rightwards arrow on top space equals space 13 over 11 straight a with rightwards arrow on top

Also,     open vertical bar straight c with rightwards arrow on top close vertical bar space equals space 13 over 11 open vertical bar straight a with rightwards arrow on top close vertical bar space space space space rightwards double arrow space space space space space space space open vertical bar straight c with rightwards arrow on top close vertical bar space greater than space open vertical bar straight a with rightwards arrow on top close vertical bar.
(ii) straight c with rightwards arrow on top space equals space 3 space straight a with rightwards arrow on top space plus space 4 space straight b with rightwards arrow on top space equals space 3 space open parentheses negative 11 over 5 straight b with rightwards arrow on top close parentheses space plus space 4 space straight b with rightwards arrow on top                     open square brackets because space space of space left parenthesis 1 right parenthesis close square brackets
       equals space minus 33 over 5 straight b with rightwards arrow on top space plus space 4 space straight b with rightwards arrow on top space equals space minus 13 over 5 straight b with rightwards arrow on top
therefore space space space straight c with rightwards arrow on top space and space straight b with rightwards arrow on top space have space opposite space directions. space
Also,                open vertical bar straight c with rightwards arrow on top close vertical bar space equals space 13 over 5 open vertical bar straight b with rightwards arrow on top close vertical bar space space space space space space space space space space rightwards double arrow space space space space space space space open vertical bar straight c with rightwards arrow on top close vertical bar space greater than space open vertical bar straight b with rightwards arrow on top close vertical bar.

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