Question

find the magnitude and direction angle (in degrees) of the following vector.
v = 11 (cos(56°)i + sin(56°)j)

Explanation:

Step1: Find the magnitude

For a vector \(\mathbf{v}=r(\cos\theta\mathbf{i}+\sin\theta\mathbf{j})\), the magnitude \(||\mathbf{v}|| = r\).
Here \(r = 11\), so \(||\mathbf{v}||=11\).

Step2: Find the direction angle

For a vector \(\mathbf{v}=r(\cos\theta\mathbf{i}+\sin\theta\mathbf{j})\), the direction angle \(\alpha=\theta\).
Here \(\theta = 56^{\circ}\), so \(\alpha = 56^{\circ}\).

Answer:

The magnitude of the vector \(\mathbf{v}\) is \(11\) and the direction angle is \(56^{\circ}\).