Question

If $straight a with rightwards arrow on top space equals space 2 straight i with hat on top plus straight j with hat on top plus 3 straight k with hat on top space space space and space straight b with rightwards arrow on top space equals space 3 straight i with hat on top space plus space 5 straight j with hat on top space minus space 2 straight k with hat on top comma space then space find space open vertical bar straight a with rightwards arrow on top cross times space straight b with rightwards arrow on top close vertical bar.$

Solution

Given space that space straight a with rightwards arrow on top space equals space 2 straight i with hat on top space plus space straight j with hat on top space plus space 3 straight k with hat on top space space and space straight b with rightwards arrow on top space equals space 3 straight i with hat on top space plus space 5 straight j with hat on top space minus space 2 straight k with hat on top We space need space to space find 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 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 2 1 3 row 3 5 cell negative 2 end cell end table close vertical bar space space space equals space straight i with hat on top left parenthesis negative 2 minus 15 right parenthesis space minus space straight j with hat on top left parenthesis negative 4 minus 9 right parenthesis space plus space straight k with hat on top left parenthesis 10 minus 3 right parenthesis space space space space equals negative 17 straight i with hat on top space plus space 13 straight j with hat on top space plus space 7 straight k with hat on top Hence comma 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 17 squared plus 13 squared plus 7 squared end root space space space space space space space space equals 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 507

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