91Ó°ÊÓ

In Exercises 31-38, find (a) \(\small{\mathbf{u}} + \small{\mathbf{v}}\), (b) \(\small{\mathbf{u}} - \small{\mathbf{v}}\), and (c) \(\small{2\mathbf{u}} - \small{3\mathbf{v}}\), Then sketch each resultant vector. \(\mathbf{u} = \langle 2, 1 \rangle\), \(\mathbf{v} = \langle 1, 3 \rangle\)

In Exercises 31-40, find the angle \(\theta\) between the vectors. \(\mathbf{u} = \langle 1, 0 \rangle\) \(\mathbf{v} = \langle 0, -2 \rangle\)

In Exercises 15-32, represent the complex number graphically, and find the trigonometric form of the number. \(-8 - 5\sqrt{3}i\)

In Exercises \(25-34,\) use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. $$ A=120^{\circ}, \quad a=b=25 $$

In Exercises 25-34, use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. \(A\ =\ 120^{\circ}\), \(a\ =\ 25\), \(b\ =\ 24\)

In Exercises 31-38, find (a) \(\small{\mathbf{u}} + \small{\mathbf{v}}\), (b) \(\small{\mathbf{u}} - \small{\mathbf{v}}\), and (c) \(\small{2\mathbf{u}} - \small{3\mathbf{v}}\), Then sketch each resultant vector. \(\mathbf{u} = \langle 2, 3 \rangle\), \(\mathbf{v} = \langle 4, 0 \rangle\)

In Exercises 15-32, represent the complex number graphically, and find the trigonometric form of the number. \(-9 - 2\sqrt{10}i\)

In Exercises 31-40, find the angle \(\theta\) between the vectors. \(\mathbf{u} = \langle 3, 2 \rangle\) \(\mathbf{v} = \langle 4, 0 \rangle\)

In Exercises 33-40, use Heron's Area Formula to find the area of the triangle. \(a = 8\), \(b = 12\), \(c = 17\)

In Exercises 31-40, find the angle \(\theta\) between the vectors. \(\mathbf{u} = 3\mathbf{i} + 4\mathbf{j}\) \(\mathbf{v} = -2\mathbf{j}\)