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Question

If a=^i+^j+^k,b=^i+^j,c=^i and (a×b)×c=λa+μb, then the value of λ+μ is

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Solution

Given,(a×b)×c=λa+μb
(ac)b(bc)a=λa+μb
By comparing, we get
λ=(bc),μ=(ac)
On substituting a,b,c, we have,
λ=((^i+^j)(^i)),μ=((^i+^j+^k)(^i))
λ=1,μ=1λ+μ=1+1=0

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