VECTORS

C)60°,60° and 45°
angle with x-axis :
cosθ= A.B|A||B|=1√1+1+2=12
θ=60°
angle with y-axis :
cosθ= A.B|A||B|=1√1+1+2=12
θ=60°
angle with z-axis :
cosθ= A.B|A||B|=√2√1+1+2=1√2
θ=45°

there's an easier way...
A=√1+1+√2=2
A_x=1=2cosθ_x=>cosθ_x=1/2 =>θ_x=60°
A_y=1=2cosθ_y=>cosθ_y=1/2 =>θ_y=60°
A_z=√2=2cosθ_z=>cosθ_z=1/√2 =>θ_z=45°

45 45 & 60 °