91Ó°ÊÓ

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. $$\mathbf{w}=\langle 3,5\rangle$$

Determine whether the given pairs of vectors are orthogonal. $$\mathbf{v}=\langle 3,1\rangle, \mathbf{w}=\langle 0,1\rangle$$

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. $$A=50^{\circ}, a=10, b=8$$

Multiply or divide as indicated, and leave the answer in trigonometric form. $$\frac{4}{3}\left(\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}\right) \cdot 2\left(\cos \frac{\pi}{4}+i \sin \frac{\pi}{4}\right)$$

Convert each of the given pairs of polar coordinates to a pair of rectangular coordinates. $$\left(-3, \frac{5 \pi}{6}\right)$$

Multiply or divide as indicated, and leave the answer in trigonometric form. $$\frac{5\left(\cos \frac{\pi}{4}+i \sin \frac{\pi}{4}\right)}{2\left(\cos \frac{\pi}{6}+i \sin \frac{\pi}{6}\right)}$$

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. $$B=70^{\circ}, b=10, c=25$$

Determine whether the given pairs of vectors are orthogonal. $$\mathbf{v}=\langle 2,-3\rangle, \mathbf{w}=\langle-6,4\rangle$$

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. $$\mathbf{v}=\langle 1,1.5\rangle$$

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