91Ó°ÊÓ

In Exercises 13-24, find the component form and the magnitude of the vector \(\mathbf{v}\).'' Initial Point - \((-3, -5)\) Terminal Point - \((5, 1)\)

In Exercises 15-24, use the vectors \(\mathbf{u} = \langle 3, 3 \rangle\), \(\mathbf{v} = \langle -4, 2 \rangle\), and \(\mathbf{w} = \langle 3, -1 \rangle\) to find the indicated quantity. State whether the result is a vector or a scalar. \((3\mathbf{w} \cdot \mathbf{v}) \mathbf{u}\)

In Exercises 15-32, represent the complex number graphically, and find the trigonometric form of the number. \(-2(1 + \sqrt{3}i)\)

In Exercises 5-20, use the Law of Cosines to solve the triangle. Round your answers to two decimal places. \(C = 43^{\circ}\), \(a = \frac{4}{9}\), \(b = \frac{7}{9}\)

In Exercises 5-20, use the Law of Cosines to solve the triangle. Round your answers to two decimal places. \(C = 101^{\circ}\), \(a = \frac{3}{8}\), \(b = \frac{3}{4}\)

In Exercises 15-32, represent the complex number graphically, and find the trigonometric form of the number. \(\frac{5}{2}(\sqrt{3} - i)\)

In Exercises 15-24, use the vectors \(\mathbf{u} = \langle 3, 3 \rangle\), \(\mathbf{v} = \langle -4, 2 \rangle\), and \(\mathbf{w} = \langle 3, -1 \rangle\) to find the indicated quantity. State whether the result is a vector or a scalar. \((\mathbf{u} \cdot 2\mathbf{v}) \mathbf{w}\)

In Exercises 13-24, find the component form and the magnitude of the vector \(\mathbf{v}\).'' Initial Point - \((-2, 7)\) Terminal Point - \((5, -17)\)

In Exercises 13-24, find the component form and the magnitude of the vector \(\mathbf{v}\).'' Initial Point - \((1, 3)\) Terminal Point - \((-8, -9)\)

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