JEE Main 20264 Apr, Evening shiftMathematicsEasyVector Algebra184× since 2002Let u^\hat uu^ and v^\hat vv^ be unit vectors inclined at an acute angle such that ∣u^×v^∣=32|\hat u\times\hat v|=\frac{\sqrt3}{2}∣u^×v^∣=23. If A⃗=λu^+v^+(u^×v^)\vec A=\lambda\hat u+\hat v+(\hat u\times\hat v)A=λu^+v^+(u^×v^), then λ\lambdaλ is equal to:AOption A. 43(A⃗⋅u^)−23(A⃗⋅v^)\frac43(\vec A\cdot\hat u)-\frac23(\vec A\cdot\hat v)34(A⋅u^)−32(A⋅v^)BOption B. 23(A⃗⋅u^)−13(A⃗⋅v^)\frac23(\vec A\cdot\hat u)-\frac13(\vec A\cdot\hat v)32(A⋅u^)−31(A⋅v^)COption C. 43(A⃗⋅u^)+23(A⃗⋅v^)\frac43(\vec A\cdot\hat u)+\frac23(\vec A\cdot\hat v)34(A⋅u^)+32(A⋅v^)DOption D. (A⃗⋅u^)−12(A⃗⋅v^)(\vec A\cdot\hat u)-\frac12(\vec A\cdot\hat v)(A⋅u^)−21(A⋅v^)CheckSkip · show solution
