91Ó°ÊÓ

\(v=\frac{3}{2} \mathbf{u}\)

In Exercises 47-52, determine whether \(\mathbf{u}\) and \(\mathbf{v}\) are orthogonal, parallel, or neither. $$ \begin{aligned} &\mathbf{u}=\langle-12,30\rangle \\ &\mathbf{v}=\left\langle\frac{1}{2},-\frac{5}{4}\right\rangle \end{aligned} $$

The lengths of the sides of a triangular parcel of land are approximately 200 feet, 500 feet, and 600 feet. Approximate the area of the parcel.

A parking lot has the shape of a parallelogram (see figure). The lengths of two adjacent sides are 70 meters and 100 meters. The angle between the two sides is \(70^{\circ}\). What is the area of the parking lot?

\(v=\frac{3}{4} w\)

In Exercises 47-52, determine whether \(\mathbf{u}\) and \(\mathbf{v}\) are orthogonal, parallel, or neither. $$ \begin{aligned} &\mathbf{u}=\langle 3,15\rangle \\ &\mathbf{v}=\langle-1,5\rangle \end{aligned} $$

Geometry You want to buy a triangular lot measuring 510 yards by 840 yards by 1120 yards. The price of the land is \(\$ 2000\) per acre. How much does the land cost?

In Exercises 47-52, determine whether \(\mathbf{u}\) and \(\mathbf{v}\) are orthogonal, parallel, or neither. $$ \begin{aligned} &\mathbf{u}=\frac{1}{4}(3 \mathbf{i}-\mathbf{j}) \\ &\mathbf{v}=5 \mathbf{i}+6 \mathbf{j} \end{aligned} $$

In Exercises 49-52, use the fundamental trigonometric identities to simplify the expression. $$ \sin x \cot x $$

In Exercises 47-52, determine whether \(\mathbf{u}\) and \(\mathbf{v}\) are orthogonal, parallel, or neither. $$ \begin{aligned} &\mathbf{u}=\mathbf{i} \\ &\mathbf{v}=-2 \mathbf{i}+2 \mathbf{j} \end{aligned} $$