If $straight theta$ is the angle between any two vectors $straight a with rightwards arrow on top space and space straight b with rightwards arrow on top comma$ then $open vertical bar straight a with rightwards arrow on top. space straight b with rightwards arrow on top close vertical bar space equals space open vertical bar straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top close vertical bar$ when $straight theta$ is equal to

0

$straight pi over 4$
$straight pi over 2$
$straight pi$

Solution

straight pi over 4

straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals 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

rightwards double arrow space space space space space space space space straight a space straight b space cos space straight theta space equals space straight a space straight b space sin space straight theta rightwards double arrow space space space space space space space fraction numerator sin space straight theta over denominator cos space straight theta end fraction space equals space 1 space space space space space space space rightwards double arrow space space space space space tan space straight theta space equals space 1 space space rightwards double arrow space space space space straight theta space equals space space straight pi over 4 therefore space space space left parenthesis straight B right parenthesis space is space correct space answer.

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