The scalars l and m such that `lveca + m vecb =vecc, " where " veca, vecb and vecc` are given vectors, are equal to

If (veca xx vecb) xx vecc = veca xx (vecb xx vecc) where veca, vecb and vecc are any three vectors such that veca.vecb =0, vecb.vecc=0 then veca and vecc are:

If (veca xx vecb) xx vecc = vec a xx (vecb xx vecc) , where veca, vecb and vecc are any three vectors such that veca.vecb ne 0, vecb.vecc ne 0 , then veca and vecc are:

Let veca , vecb,vecc be three vectors such that veca bot ( vecb + vecc), vecb bot ( vecc + veca) and vecc bot ( veca + vecb) , " if " |veca| =1 , |vecb| =2 , |vecc| =3 , " then " | veca + vecb + vecc| is,

Let veca , vecb,vecc be three vectors such that veca bot ( vecb + vecc), vecb bot ( vecc + veca) and vecc bot ( veca + vecb) , " if " |veca| =1 , |vecb| =2 , |vecc| =3 , " then " | veca + vecb + vecc| is,

veca.(vecbxxvecc) is called the scalar triple product of veca,vecb,vecc and is denoted by [veca vecb vecc]. If veca, vecb, vecc are cyclically permuted the vaslue of the scalar triple product remasin the same. In a scalar triple product, interchange of two vectors changes the sign of scalar triple product but not the magnitude. in scalar triple product the the position of the dot and cross can be interchanged privided the cyclic order of vectors is preserved. Also the scaslar triple product is ZERO if any two vectors are equal or parallel. [veca+vecb vecb+vecc vecc+veca] is equal to (A) 2[veca vecb vecc] (B) 3[veca,vecb,vecc] (C) [veca,vecb,vecc] (D) 0

If veca , vecb and vecc are three vectors such that vecaxx vecb =vecc, vecb xx vecc= veca, vecc xx veca =vecb then prove that |veca|= |vecb|=|vecc|

If veca , vecb and vecc are three vectors such that vecaxx vecb =vecc, vecb xx vecc= veca, vecc xx veca =vecb then prove that |veca|= |vecb|=|vecc|

If veca , vecb and vecc are three vectors such that vecaxx vecb =vecc, vecb xx vecc= veca, vecc xx veca =vecb then prove that |veca|= |vecb|=|vecc|