find the direction of the resultant vector.\n(14, 7)\nθ = ?°\n(-9, -2)\nround to the nearest hundredth.

Explanation:

Step1: Find the resultant vector components

To find the resultant vector (\vec{r}), we add the corresponding components of (\vec{v}) and (\vec{w}). Given (\vec{v}=(14,7)) and (\vec{w}=(-9,-2)), the resultant vector (\vec{r}=\vec{v}+\vec{w}). The (x)-component of (\vec{r}) is (14 + (-9)=14 - 9 = 5). The (y)-component of (\vec{r}) is (7+(-2)=7 - 2 = 5). So, (\vec{r}=(5,5)).

Step2: Calculate the angle (\theta)

The direction of a vector ((x,y)) is given by (\theta=\arctan\left(\frac{y}{x}\right)) (since both (x = 5) and (y = 5) are positive, the vector is in the first quadrant). Substitute (x = 5) and (y = 5) into the formula: (\theta=\arctan\left(\frac{5}{5}\right)=\arctan(1)). We know that (\arctan(1) = 45^{\circ}) (since (\tan(45^{\circ})=1)).

Answer:

(45.00)