A) 25
B) \[6\sqrt{11}\]
C) \[11\sqrt{5}\]
D) \[11\sqrt{6}\]
E) \[5\sqrt{11}\]
Correct Answer: D
Solution :
Given, \[|\overrightarrow{a}|=5,|\overrightarrow{b}|=6,\overrightarrow{a}.\overrightarrow{b}=-25\] \[\therefore \]\[\cos \theta =\frac{\overrightarrow{a}.\overrightarrow{b}}{|\overrightarrow{a}|.|\overrightarrow{b}|}=\frac{-25}{5\times 6}=-\frac{25}{30}=-\frac{5}{6}\] \[\therefore \]\[\sin \theta =\sqrt{1-{{\cos }^{2}}\theta }=\sqrt{1-\frac{25}{36}}\] \[=\sqrt{\frac{11}{36}}\] \[\therefore \] \[|\overrightarrow{a}\times \overrightarrow{b}|=|\overrightarrow{a}|\,|\overrightarrow{b}|\sin \theta |\] \[=5\times 6\times \sqrt{\frac{11}{36}}\] \[=5\sqrt{11}\]
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