Question

1. find the direction angle of v.

v = -5i - 5j

Explanation:

Step1: Identify the components of the vector

Given \(v=-5i - 5j\), so \(x=-5\) and \(y = -5\).

Step2: Calculate the tangent of the direction angle

Use the formula \(\tan\theta=\frac{y}{x}\). Substitute \(x=-5\) and \(y = -5\) into it: \(\tan\theta=\frac{-5}{-5}=1\).

Step3: Determine the direction angle

Since \(x<0\) and \(y<0\), the vector is in the third - quadrant. We know that \(\tan\theta = 1\) gives \(\theta=\arctan(1)+180^{\circ}\). Because \(\arctan(1) = 45^{\circ}\), so \(\theta=45^{\circ}+180^{\circ}\).

Answer:

\(225^{\circ}\)