question_answer

Let \[\overset{\to }{\mathop{a}}\,,\overset{\to }{\mathop{b}}\,\] and \[\overset{\to }{\mathop{c}}\,\] be three vectors such that \[\left| \overset{\to }{\mathop{a}}\, \right|=\sqrt{3},\] \[\left| \overset{\to }{\mathop{b}}\, \right|=5,\] \[\overset{\to }{\mathop{b}}\,.\overset{\to }{\mathop{c}}\,=10\] and the angle between \[\overset{\to }{\mathop{b}}\,\] and \[\overset{\to }{\mathop{c}}\,\] is \[\frac{\pi }{3}.\] If \[\overset{\to }{\mathop{a}}\,\] is perpendicular to the vector \[\overset{\to }{\mathop{b}}\,\times \overset{\to }{\mathop{c}}\,,\] then \[\left| \overset{\to }{\mathop{a}}\,\times \left( \overset{\to }{\mathop{b}}\,\times \overset{\to }{\mathop{c}}\, \right) \right|\] is equal to ________. [JEE MAIN Held on 09-01-2020 Evening]

Answer:

30