find the direction of the resultant vector.\nround to the nearest hundredth.

Explanation:

Step1: Find the resultant vector components

To find the resultant vector (\vec{r}=\vec{v}+\vec{w}), we add the corresponding components of (\vec{v}=(6,8)) and (\vec{w}=(-4,12)). The (x)-component of the resultant vector (r_x = 6+(-4)=2) The (y)-component of the resultant vector (r_y = 8 + 12=20)

Step2: Calculate the angle (\theta)

The direction of a vector ((x,y)) is given by (\theta=\arctan\left(\frac{y}{x}\right)) (when (x>0), which is the case here since (r_x = 2>0)). So we calculate (\theta=\arctan\left(\frac{20}{2}\right)=\arctan(10))

Using a calculator, (\arctan(10)\approx84.29^{\circ})

Answer:

(84.29)