the vector a x(b x c),b x(c x a) and c x(a x b)are a)coplanar b)collinear c)non coplanar d)non colliear - Maths - Vector Algebra

Question

​the vector​ a x(b x c),b x(c x a) and
c x(a x b)are a)coplanar b)collinear c)non coplanar d)non colliear
???/

Priyanka Kedia · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

a×b×c+b×c×a+c×a×b=a·cb-a·bc+b·ac-b·ca+c·ba-c·ab                                                        =a·cb-a·bc+a·bc-b·ca+b·ca-a·cb                   a·c=c·a, b·c=c·b, a·b=b·a                                                        =0⇒a×b×c+b×c×a+c×a×b=0Since their exist a linear relation between all three vector therefore they can be expressed as a linear combination of other two
Hence these three vectors are coplanar

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​the vector​ a x(b x c),b x(c x a) and c x(a x b)are a)coplanar b)collinear c)non coplanar d)non colliear ???/

the vector a x(b x c),b x(c x a) and c x(a x b)are a)coplanar b)collinear c)non coplanar d)non colliear ???/