For any vector 'a' show that : ix(axi) + jx(axj) + kx(axk)=2a

Asked by DIVYA GARG | 6th Jun, 2013, 01:35: PM

Expert Answer:

Let a = mi + nj+ok
 
Then, ix(axi) + jx(axj) + kx(axk) = 
i x ((mi + nj+ok) x i) + j x ((mi + nj+ok) x j) + k x ((mi + nj+ok) x k)
= i x (-nk + oj) + j x (mk -oi) + k x (-mj+ni)
= nj + ok + mi + ok+ mi + nj
= 2(mi + nj+ok)
= 2a
= RHS

Answered by  | 7th Jun, 2013, 02:00: AM

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