A) \[3\]
B) \[4\]
C) \[5\]
D) \[6\]
Correct Answer: D
Solution :
Given, \[|a|=2,\,\,|b|=5\] \[\because \] \[a\times b=|a|\,|b|\,\sin \,\theta .n\] \[\Rightarrow \] \[|a\times b|=|a|\,\,|b|\,\sin \theta .1\] \[(\because \,\,|n|=1\,)\] \[\Rightarrow \] \[8=2\times 5.\sin \theta \] \[[\because \,\,|a\times b|\,=8\,\,(given)]\] \[\Rightarrow \] \[\sin \,\theta =\frac{4}{5}\] \[\therefore \] \[\cos \,\,\theta =\sqrt{1-{{\left( \frac{4}{5} \right)}^{2}}}\,=\sqrt{\frac{9}{25}}=\frac{3}{2}\] Now, \[a\,.\,b\,\,=\,|a|\,|b|\,\,cos\,\theta \] \[\Rightarrow \] \[a\,.\,b=2\times 5\times \frac{3}{5}=6\]
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