(Solved): Consider the vectors in the figure. Give the length of the required vector and indicate the directi ...

Consider the vectors in the figure. Give the length of the required vector and indicate the direction by giving the acute angle $\beta$ it makes with $w$. When calculating angles between the vectors, make sure they share a common base. This exercise requires decimal approximations, so different methods of finding a solution may lead to slightly different answers (which is perfectly acceptable). Find the length and direction of $\mathbf{v}+\mathbf{w}$ if $\Vert \mathbf{v}\Vert =1,\Vert \mathbf{w}\Vert =6$, and $\alpha =30^{\circ }$ (Use decimal notation. Give your answers to two decimal places. Include the degree symbol in your answer where needed.)