91Ó°ÊÓ

In Exercises \(59-64\), evaluate the expression without using a calculator. $$ \arctan (-\sqrt{3}) $$

In Exercises 59-62, find two vectors in opposite directions that are orthogonal to the vector u. (There are many correct answers.) $$ \mathbf{u}=-\frac{5}{2} \mathbf{i}-3 \mathbf{j} $$

\(\|\mathbf{v}\|=4 \sqrt{3} \quad \theta=90^{\circ}\)

\(\|\mathbf{v}\|=2 \quad \mathbf{v}\) in the direction \(\mathbf{i}+3 \mathbf{j}\)

Work In Exercises 63 and 64, find the work done in moving a particle from \(P\) to \(Q\) if the magnitude and direction of the force are given by \(\mathbf{v}\). $$ P=(0,0), \quad Q=(4,7), \quad \mathbf{v}=\langle 1,4\rangle $$

In Exercises \(59-64\), evaluate the expression without using a calculator. $$ \arcsin \left(-\frac{\sqrt{3}}{2}\right) $$

\(\|\mathbf{v}\|=3 \quad \mathbf{v}\) in the direction \(3 \mathbf{i}+4 \mathbf{j}\)

In Exercises \(59-64\), evaluate the expression without using a calculator. $$ \arccos \left(-\frac{\sqrt{3}}{2}\right) $$

Work In Exercises 63 and 64, find the work done in moving a particle from \(P\) to \(Q\) if the magnitude and direction of the force are given by \(\mathbf{v}\). $$ P=(1,3), \quad Q=(-3,5), \quad \mathbf{v}=-2 \mathbf{i}+3 \mathbf{j} $$

The vector \(\mathbf{u}=\langle 1650,3200\rangle\) gives the numbers of units of two types of baking pans produced by a company. The vector \(\mathbf{v}=\langle 15.25,10.50\rangle\) gives the prices (in dollars) of the two types of pans, respectively. (a) Find the dot product \(\mathbf{u} \cdot \mathbf{v}\) and interpret the result in the context of the problem. (b) Identify the vector operation used to increase the prices by \(5 \%\).