Find the angle between the vectors:

$straight A with rightwards arrow on top equals straight i with hat on top plus space 2 straight j with hat on top minus straight k with hat on top space$ and $straight B with rightwards arrow on top space equals space minus straight i with hat on top plus straight j with hat on top minus 2 straight k with hat on top$

Solution

Angle between the vectors is given by,
$cos space theta space equals space fraction numerator A with rightwards harpoon with barb upwards on top space. space B with rightwards harpoon with barb upwards on top over denominator A B end fraction space space space space space space space space space space space space equals fraction numerator space left parenthesis i with hat on top space plus space 2 j with hat on top space minus k with hat on top right parenthesis space. space left parenthesis negative i with hat on top space plus space j with hat on top space minus 2 k with hat on top right parenthesis over denominator 6 end fraction space space space space space space space space space space space equals space fraction numerator negative 1 space plus space 2 space plus space 2 over denominator 6 end fraction space equals space 3 over 6 space equals space 1 half$
That is $straight theta$ = cos^-1 $1 half$
This implies,
$straight theta$ = 60⁰