Question

find a.b if |a| =2 and |b| =5 and |a×b|=8​

Answer 1

$heya \\ \\ \\ a.b = |a| \times |b| \times \cos( \alpha ) \\ \\ \\ and \\ \\ \\ \\ a \times b = |a| \times |b| \times \sin( \alpha ) \\ \\ \\ \\ where \: \alpha \: \: is \: the \: angle \: between \: a \: and \: b \: \\ \\ \\ \\ 8 \div 10 = \ \sin( \alpha ) \\ \\ \\ \sin( \alpha ) = 4 \div 5 \\ \\ \\ and \: \: \: \: \cos( \alpha ) = 3 \div 5 \\ \\ \\ \\ so \: \: a.b = 5 \times 2 \times 3 \div 5 \\ \\ \\ a.b = 6$