a→ and b→  are two unit vectors that are mutually perpendicular. A unit vector that is equally inclined to a→,b→ and a→×b→ is

Let the required vector r→ be such that r→=x1a→+x2b→+x3a→×b→We must have r→⋅a→=r→⋅b→=r→⋅(a→×b→)  (as r→,a→,b→ and a→×b→ are unit vectors and r→ is equally inclined to  a→,b→ and a→×b→)now  r→⋅a→=x1,r→⋅b→=x2,r→⋅(a→×b→)=x3⇒r→=λ(a→+b→+(a→×b→))also,  r→⋅r→=1⇒λ2(a→+b→+a→×b→)⋅(a→+b→+(a→×b→))=1or  λ2|a→|2+|b→|2+|a→×b→|2=1or  λ2=13or λ=±13⇒ r→=±13(a→+b→+a→×b→)