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 …. 

Similarly,

l2l3 + m2m3 + n2n3 = 0 …. 

l1l3 + m1m3 + n1n3 = 0 …. 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 …. 

Hence, putting values from , ,  and  we have Hence Proved!

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