91Ó°ÊÓ

Find (a) \(\mathbf{u}+\mathbf{v}\) (b) \(\mathbf{u}-\mathbf{v},(\mathbf{c})\) 2 \(\mathbf{u}-3 \mathbf{v},\) and (d) \(\frac{1}{2} \mathbf{v}+4 \mathbf{u} .\) Then sketch each resultant vector.$$\mathbf{u}=\langle 5,3\rangle, \mathbf{v}=\langle-4,0\rangle$$

Represent the complex number graphically, and find the trigonometric form of the number. $$6$$

Use vectors to find the interior angles of the triangle with the given vertices. $$(-3,5), (-1,9), (7,9)$$

Determine whether the Law of sines or the Law of cosines can be used to find another measure of the triangle. Then solve the triangle. $$C=95^{\circ}, \quad b=19, \quad c=25$$

Find \(\mathbf{u} \cdot \mathbf{v},\) where \(\theta\) is the angle between \(\mathbf{u}\) and \(\mathbf{v}.\) $$\|\mathbf{u}\|=9,\|\mathbf{v}\|=36, \theta=\frac{3 \pi}{4}$$

Find (a) \(\mathbf{u}+\mathbf{v}\) (b) \(\mathbf{u}-\mathbf{v},(\mathbf{c})\) 2 \(\mathbf{u}-3 \mathbf{v},\) and (d) \(\frac{1}{2} \mathbf{v}+4 \mathbf{u} .\) Then sketch each resultant vector.$$\mathbf{u}=\langle-6,-8\rangle, \mathbf{v}=\langle 2,4\rangle$$

Find the area of the triangle having the indicated angle and sides. \(B=75^{\circ} 15^{\prime}, \quad a=103, \quad c=58\)

Represent the complex number graphically, and find the trigonometric form of the number. $$3+\sqrt{3} i$$

Use Heron's Area Formula to find the area of the triangle. $$a=12, \quad b=24, \quad c=18$$

Find (a) \(\mathbf{u}+\mathbf{v}\) (b) \(\mathbf{u}-\mathbf{v},(\mathbf{c})\) 2 \(\mathbf{u}-3 \mathbf{v},\) and (d) \(\frac{1}{2} \mathbf{v}+4 \mathbf{u} .\) Then sketch each resultant vector.$$\mathbf{u}=\langle 0,-5\rangle, \mathbf{v}=\langle-4,10\rangle$$