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Vector Algebra

Question
CBSEENMA12034060
Wired Faculty App

Find the angle between the vectors straight i with hat on top space minus space 2 space straight j with hat on top space plus space 3 space straight k with hat on top space and space 3 space straight i with hat on top space minus space 2 space straight j with hat on top space plus space straight k with hat on top.

Solution
Let straight theta be the angle between vectors
              straight a with rightwards arrow on top space equals space straight i with hat on top space minus space 2 space straight j with hat on top space plus space 3 space straight k with hat on top space space and space straight b with rightwards arrow on top space equals space 3 space straight i with hat on top space minus space 2 space straight j with hat on top space plus space straight k with hat on top
Now,  straight a space equals space square root of 1 plus 4 plus 9 end root space equals square root of 14 comma space space space straight b space equals space square root of 9 plus 4 plus 1 end root space equals space square root of 14
                straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space left parenthesis 1 right parenthesis thin space left parenthesis 3 right parenthesis space plus space left parenthesis negative 2 right parenthesis thin space left parenthesis negative 2 right parenthesis space plus space left parenthesis 3 right parenthesis thin space left parenthesis 1 right parenthesis space equals space 3 plus 4 plus 3 space equals space 0
Now straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space straight a space straight b space cos space straight theta space space space rightwards double arrow space space space space 10 space equals space left parenthesis square root of 14 right parenthesis thin space left parenthesis square root of 14 right parenthesis space cos space straight theta
therefore space space space space space space space cos space straight theta space equals space 10 over 14 space equals space 5 over 7 space space space space rightwards double arrow space space space space straight theta space equals space cos to the power of negative 1 end exponent open parentheses 5 over 7 close parentheses

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