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Vector Algebra

Question
CBSEENMA12034167
Wired Faculty App

Find open vertical bar straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top close vertical bar  if  straight a with rightwards arrow on top space equals straight i with hat on top space minus space 7 space straight j with hat on top space plus space 7 space straight k with hat on top and straight b with rightwards arrow on top space equals space 3 straight i with hat on top space minus space 2 straight j with hat on top space plus space 2 straight k with hat on top

Solution

Here,   straight a with rightwards arrow on top space equals straight i with hat on top space minus space 7 space straight j with hat on top space plus space 7 space straight k with hat on top comma space space straight b with rightwards arrow on top space equals 3 space straight i with hat on top space minus space 2 space straight j with hat on top space plus space 2 space straight k with hat on top
therefore space space space straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top space equals space open vertical bar table row cell straight i with hat on top end cell cell straight j with hat on top end cell cell straight k with hat on top end cell row 1 cell negative 7 end cell 7 row 3 cell negative 2 end cell 2 end table close vertical bar space equals space straight i with hat on top space open vertical bar table row cell negative 7 end cell 7 row cell negative 2 end cell 2 end table close vertical bar space minus space straight j with hat on top space open vertical bar table row 1 7 row 3 2 end table close vertical bar space plus space straight k with hat on top space open vertical bar table row 1 cell negative 7 end cell row 3 cell negative 2 end cell end table close vertical bar
                      equals space left parenthesis negative 14 plus 14 right parenthesis space straight i with hat on top space minus space left parenthesis 2 minus 21 right parenthesis space straight j with hat on top space plus space left parenthesis negative 2 plus 21 right parenthesis space straight k with hat on top space equals space 19 space straight j with hat on top space plus space 19 space straight k with hat on top
therefore space space space open vertical bar straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top close vertical bar space equals space square root of left parenthesis 0 right parenthesis squared plus left parenthesis 19 right parenthesis squared plus left parenthesis 19 right parenthesis squared end root space equals square root of 0 plus 381 plus 381 end root space equals space square root of 2 space cross times 381 end root space equals space 19 square root of 2

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