Questions: What is the direction of w? Round to the nearest hundredth.

Solution Steps

The vector \(\vec{w}\) has its tail at the origin and its head at the point \((-5, 2)\). Therefore, the components of the vector \(\vec{w}\) are:

• \(x = -5\)
• \(y = 2\)

The direction angle \(\theta\) of the vector \(\vec{w}\) can be found using the arctangent function: \[ \theta = \tan^{-1}\left(\frac{y}{x}\right) \] Substitute the values of \(x\) and \(y\): \[ \theta = \tan^{-1}\left(\frac{2}{-5}\right) \]

Calculate the arctangent: \[ \theta = \tan^{-1}\left(-0.4\right) \approx -21.80^\circ \] Since the vector is in the second quadrant (negative x and positive y), we need to add 180° to the angle: \[ \theta = -21.80^\circ + 180^\circ = 158.20^\circ \]

Final Answer