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Question

If a,b,c are unit vectors such that a.b=0 and (ac).(b+c)=0 and c=λa+μb+ω(a×b) for some scalars λ,μ,ω, then
  1. μ=λ+1
  2. λ2+μ2+ω2=2
  3. λ2+μ2+ω2=1
  4. λ=μ+1


Solution

The correct options are
C λ2+μ2+ω2=1
D λ=μ+1
a.b=0a×b is a unit vector.

c.a=λ, c.b=μ

c.(a×b)=ω

(ac).(b+c)=0λμ1=0

λ=μ+1

|c|2=λ2|a|2+μ2|b|2+w2|a×b|2

(a,b,a×bare orthogonal pairs of unit vectors)

1=λ2+μ2+w2

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