| Direction: Let a, b and c be three vectors such that \[|a|\,=\,|b|\,=\,|\,c|\,=4\]and the angle between a and b is \[\pi /3,\] the angle between b and c is \[\pi /3,\] and angle between c and a is \[\pi /3,\]. Then, |
A) \[4\sqrt{\frac{2}{3}}\]
B) \[3\sqrt{\frac{2}{3}}\]
C) \[4\sqrt{\frac{3}{2}}\]
D) \[3\sqrt{\frac{3}{2}}\]
Correct Answer: A
Solution :
Volume of the parallel piped = (base area) \[\times \] high \[\Rightarrow \] \[32\sqrt{2}=2\times \left( \frac{1}{2}\times 4\times 4\times \sin \,\frac{\pi }{3} \right)\times h\] \[\Rightarrow \] \[h=4\sqrt{\frac{2}{3}}\]
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