91Ó°ÊÓ

Determine whether the given pairs of vectors are orthogonal. $$\mathbf{v}=\langle-5,2\rangle, \mathbf{w}=\langle 4,-10\rangle$$

Find the magnitude and direction of each of the given vectors. Express the direction as an angle \(\theta\) in standard position, where \(0^{\circ} \leq \theta<360^{\circ},\) to tuo decimal places. $$\mathbf{u}=\langle-1.5,3\rangle$$

Convert each of the given pairs of rectangular coordinates to a pair of polar coordinates ( \(r, \theta\) ) with \(r>0\) and \(0 \leq \theta<2 \pi\). $$(-4,-4)$$

Multiply or divide as indicated, and leave the answer in trigonometric form. $$\frac{6\left(\cos \frac{\pi}{12}+i \sin \frac{\pi}{12}\right)}{3\left(\cos \frac{\pi}{4}+i \sin \frac{\pi}{4}\right)}$$

If at least one triangle with the given characteristics exists, solve the triangle; otherwise, state that there is no solution. If there are treo solutions, give both of them. The standard notation for labeling of triangles is used. $$C=48^{\circ}, c=7, b=12$$

Find the magnitude and direction of each of the given vectors. Express the direction as an angle \(\theta\) in standard position, where \(0^{\circ} \leq \theta<360^{\circ},\) to tuo decimal places. $$\mathbf{v}=\left\langle\frac{4}{3}, \frac{2}{5}\right\rangle$$

Convert each of the given pairs of rectangular coordinates to a pair of polar coordinates ( \(r, \theta\) ) with \(r>0\) and \(0 \leq \theta<2 \pi\). $$(-\sqrt{3},-1)$$

Determine whether the given pairs of vectors are orthogonal. $$\mathbf{v}=\left\langle\frac{1}{3}, 2\right\rangle, \mathbf{w}=\left\langle 6, \frac{5}{2}\right\rangle$$

Use De Moivre's Theorem to find each expression. $$(1+i)^{4}$$

Convert each of the given pairs of rectangular coordinates to a pair of polar coordinates ( \(r, \theta\) ) with \(r>0\) and \(0 \leq \theta<2 \pi\). $$(-2,2 \sqrt{3})$$