If the vectors $bold AB space equals space 3 bold i with bold hat on top space plus 4 bold k with bold hat on top$ and $bold AC space equals space 5 bold i with bold hat on top space minus 2 bold j with hat on top plus 4 bold k with bold hat on top$ are the sides of a ΔABC, then the length of the median through A is

$square root of 18$
$square root of 72$
$square root of 33$
$square root of 45$

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Solution

square root of 33

bold AM with bar on top space space space equals space fraction numerator top enclose bold AB bold space bold plus top enclose bold AC over denominator 2 end fraction bold AM with bar on top space space space equals space 4 straight i with hat on top space minus straight j with hat on top space plus 4 straight k with hat on top vertical line bold AM with bar on top space vertical line space equals space square root of 16 plus 16 plus 1 end root space equals space square root of 33

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