91Ó°ÊÓ

Finding the Angle Between Two Vectors In Exercises \(31-40,\) find the angle \(\theta\) between the vectors. $$\mathbf{u}=2 \mathbf{i}-3 \mathbf{j}$$ $$\mathbf{v}=4 \mathbf{i}+3 \mathbf{j}$$

Using Heron's Area Formula use Heron's Area Formula to find the area of the triangle. $$ a=33, \quad b=36, \quad c=25 $$

Writing a Complex Number in Standard Form In Exercises \(31-40\) , write the standard form of the complex number. Then represent the complex number graphically. $$8\left(\cos \frac{\pi}{2}+i \sin \frac{\pi}{2}\right)$$

Vector Operations In Exercises 31-38, find (a) \(\mathbf{u}+\mathbf{v}\) . (b) \(\mathbf{u}-\mathbf{v},\) and \((\mathbf{c}) 2 \mathbf{u}-3 \mathbf{v} .\) Then sketch each resultant vector. $$\mathbf{u}=2 \mathbf{j}, \quad \mathbf{v}=3 \mathbf{i}$$

Finding a Unit Vector In Exercises \(39-48,\) find a unit vector in the direction of the given vector. Verify that the result has a magnitude of 1 . $$\mathbf{u}=\langle 3,0\rangle$$

Using Heron's Area Formula use Heron's Area Formula to find the area of the triangle. $$ a=2.5, \quad b=10.2, \quad c=9 $$

Finding the Angle Between Two Vectors In Exercises \(31-40,\) find the angle \(\theta\) between the vectors. $$\mathbf{u}=\cos \left(\frac{\pi}{3}\right) \mathbf{i}+\sin \left(\frac{\pi}{3}\right) \mathbf{j}$$ $$\mathbf{v}=\cos \left(\frac{3 \pi}{4}\right) \mathbf{i}+\sin \left(\frac{3 \pi}{4}\right) \mathbf{j}$$

Writing a Complex Number in Standard Form In Exercises \(31-40\) , write the standard form of the complex number. Then represent the complex number graphically. $$5\left[\cos \left(198^{\circ} 45^{\prime}\right)+i \sin \left(198^{\circ} 45^{\prime}\right)\right]$$

Finding the Area of a Triangle In Exercises \(39-46\) find the area of the triangle having the indicated angle and sides. $$C=120^{\circ}, \quad a=4, \quad b=6$$

Using Heron's Area Formula use Heron's Area Formula to find the area of the triangle. $$ a=75.4, \quad b=52, \quad c=52 $$