91Ó°ÊÓ

Find two vectors in opposite directions that are orthogonal to the vector \(\mathbf{u}.\) (There are many correct answers.) $$\mathbf{u}=\langle 2,6\rangle$$

Perform the operation and leave the result in trigonometric form. $$\left[\frac{3}{2}\left(\cos \frac{\pi}{6}+i \sin \frac{\pi}{6}\right)\right]\left[6\left(\cos \frac{\pi}{4}+i \sin \frac{\pi}{4}\right)\right]$$

Find two vectors in opposite directions that are orthogonal to the vector \(\mathbf{u}.\) (There are many correct answers.) $$\mathbf{u}=\langle-7,5\rangle$$

Evaluate the expression without using a calculator. $$\arccos \left(-\frac{\sqrt{3}}{2}\right)$$

Perform the operation and leave the result in trigonometric form. $$\left[\frac{5}{3}\left(\cos 140^{\circ}+i \sin 140^{\circ}\right)\right]\left[\frac{2}{3}\left(\cos 60^{\circ}+i \sin 60^{\circ}\right)\right]$$

Find two vectors in opposite directions that are orthogonal to the vector \(\mathbf{u}.\) (There are many correct answers.) $$\mathbf{u}=\frac{1}{2} \mathbf{i}-\frac{3}{4} \mathbf{j}$$

Evaluate the expression without using a calculator. $$\tan ^{-1} \frac{\sqrt{3}}{3}$$

Evaluate the expression without using a calculator. $$\tan ^{-1} \sqrt{3}$$

Find the component form of \(v\) and sketch the specified vector operations geometrically, where \(\mathbf{u}=2 \mathbf{i}-\mathbf{j}\) and \(\mathbf{w}=\mathbf{i}+2 \mathbf{j}\).$$\mathbf{v}=\frac{3}{4} \mathbf{w}$$

Perform the operation and leave the result in trigonometric form. $$\left[\frac{1}{2}\left(\cos 115^{\circ}+i \sin 115^{\circ}\right)\right]\left[\frac{4}{5}\left(\cos 300^{\circ}+i \sin 300^{\circ}\right)\right]$$