Identify the Surface with the Vector Equation (Hint: First Consider

Short Answer

Identify the surface with the vector equation $\mathbf { r } ( u , v ) = \cos u \sin v \mathbf { i } + \sin u \sin v \mathbf { j } + \cos v \mathbf { k } , 0 \leq u \leq 2 \pi , 0 \leq v \leq \frac { \pi } { 2 }$ . (Hint: First consider $x ^ { 2 } + y ^ { 2 }$ .)