Question

If $straight a with rightwards arrow on top space equals space straight i with hat on top space plus space straight j with hat on top space minus space 3 space straight k with hat on top space and space straight b with rightwards arrow on top space equals 3 space straight i with hat on top space minus space 2 space straight j with hat on top space plus space 2 space straight k with hat on top comma space space find space open vertical bar 2 straight b with rightwards arrow on top cross times space straight a with rightwards arrow on top close vertical bar.$

Solution

space straight a with rightwards arrow on top space equals straight i with hat on top space plus space straight j with hat on top space minus space 3 space straight k with hat on top space straight b with rightwards arrow on top space equals space straight j with hat on top space plus space 2 space straight k with hat on top space space space space space space space space space space space rightwards double arrow space space space space 2 space straight b with rightwards arrow on top space equals space 2 space straight j with hat on top space plus space 4 space straight k with hat on top

therefore space space 2 space straight b with rightwards arrow on top space cross times space straight a 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 0 2 4 row 1 1 cell negative 3 end cell end table close vertical bar space equals space straight i with hat on top space open vertical bar table row 2 4 row 1 cell negative 3 end cell end table close vertical bar space minus space stack straight j space with hat on top open vertical bar table row 0 4 row 1 cell negative 3 end cell end table close vertical bar space plus straight k with hat on top space open vertical bar table row 0 2 row 1 1 end table close vertical bar space space space space space space space space space space space space space space space space space space space space space equals space left parenthesis negative 6 minus 4 right parenthesis space straight i with hat on top space minus space left parenthesis 0 minus 4 right parenthesis space straight j with hat on top space plus space left parenthesis 0 minus 2 right parenthesis space straight k with hat on top space equals space minus 10 space straight i with hat on top plus 4 space straight j with hat on top space minus space 2 space straight k with hat on top

equals space 2 left parenthesis negative 5 space straight i with hat on top space plus space 2 space straight j with hat on top space minus space straight k with hat on top right parenthesis

therefore space space space open vertical bar 2 straight b with rightwards arrow on top space cross times space straight a with rightwards arrow on top close vertical bar space equals 2 space square root of left parenthesis negative 5 right parenthesis squared plus left parenthesis 2 right parenthesis squared plus left parenthesis negative 1 right parenthesis squared end root space equals space 2 square root of 25 plus 4 plus 1 end root space equals space 2 square root of 30

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