Let a→⋅b→=0, where a→ and b→ are unit vectors and the unit vector c→ is inclined at an angle θ to both a→ and b→. If c→=ma→+nb→+p(a→×b→),(m,n,p∈R) then

c→=ma→+nb→+p(a→×b→)Taking dot product with a→ and b→ we have m=n=cosθ⇒ |c→|=|cos⁡θa→+cos⁡θb→+p(a→×b→)|=1Squaring both sides, we get cos2⁡θ+cos2⁡θ+p2=1or   cos⁡θ=±1−p22now  −12≤cos⁡θ≤12 ( for real value of θ)π4≤θ≤3π4