(a) Find a vector … at a … angle with … and…

(a) Find a vector $\mathbf{V}$ at a $45^{\circ }$ angle with $\mathbf{i}$ and $\mathbf{j}$.
(b) Find $\mathbf{W}$ that makes a $60^{\circ }$ angle with $\mathbf{i}$ and $\mathbf{j}$.
(c) Explain why no vector makes a $30^{\circ }$ angle with $\mathbf{i}$ and $\mathbf{j}$.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §11.1 Vectors and Dot Products, #46