question_answer

If \[[\vec{a}\,\,\vec{b}\,\,\vec{c}]=1,\]then the value of is \[[\vec{a}\times (\vec{b}+\vec{c})\,\,\,\vec{b}\times (\vec{c}-2\vec{a})\,\,\vec{c}\times (\vec{a}+3\vec{b})]\]

A) \[3\]                       

B)        \[5\]                       

C) \[6\]                       

D)        \[7\]

Correct Answer: D

Solution :

[d] Let \[\overset{\to }{\mathop{a}}\,\times \overset{\to }{\mathop{b}}\,=\overset{\to }{\mathop{l}}\,,\overset{\to }{\mathop{b}}\,\times \overset{\to }{\mathop{c}}\,=\overset{\to }{\mathop{m}}\,,\overset{\to }{\mathop{c}}\,\times \overset{\to }{\mathop{a}}\,=\overset{\to }{\mathop{n}}\,\] \[\therefore \] Given product is \[=7\,{{[\vec{a}\,\,\vec{b}\,\,\vec{c}]}^{2}}\]