Q. 6

Let <span lang="E

Answer :

Let the magnitude of three vectors be r1, r2 and r3 respectively.


Then, three perpendicular vectors will be





As, vectors are mutually perpendicular, dot product of any two vectors will be zero


v1. v2 = l1r1l2r2 + m1r1m2r2 + n1r1n2r2 = 0


l1l2 + m1m2 + n1n2 = 0 …. [1]


Similarly,


l2l3 + m2m3 + n2n3 = 0 …. [2]


l1l3 + m1m3 + n1n3 = 0 …. [3]



Now, If A = [aij]m × n then A’ = [aji]n × m


Therefore,





Now, as li, mi and ni are direction cosiner


li2 + mi2 + ni2 = 1 …. [4]


Hence, putting values from [1], [2], [3] and [4] we have



Hence Proved!


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