Question

find the magnitude and direction angle (in degrees) of the following vector.

v = 7(cos(80°)i + sin(80°)j)

Explanation:

Step1: Find the magnitude

The vector is given in the form \(v = a(\cos\theta i+\sin\theta j)\). The magnitude of the vector \(v\) is given by the formula \(|v|=a\).
Here \(a = 7\), so \(|v|=7\).

Step2: Find the direction angle

The direction angle \(\theta\) of the vector \(v=a(\cos\theta i+\sin\theta j)\) is the angle inside the trigonometric functions.
Here \(\theta = 80^{\circ}\)

Answer:

The magnitude of the vector is \(7\) and the direction angle is \(80^{\circ}\)