If |a| , = 2, , ,|b| , = 5 and |a b| , = 8, then a . b is equal t… - Vidyadip

MCQ

If $|a|\, = 2,\,\,|b|\, = 5$ and $|a \times b|\, = 8,$ then $a . b $ is equal to

A
$0$
B
$2$
C
$4$
✓
$6$

✓

Answer

Correct option: D.

$6$

d
(d) $a\,.\,b = \,|a|\,|b|\cos \theta $; But $|a \times b|\, = \,|a|\,|b|\,\sin \theta $

$ \Rightarrow \sin \theta = \frac{{|a \times b|}}{{|a|\,|b|}} = \frac{4}{5} \Rightarrow \cos \theta = \frac{3}{5}$

Therefore, $a\,.\,b = 2 \times 5 \times \frac{3}{5} = 6.$

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