1. **State the problem:** Find the sum of the vectors $\langle 7, -2 \rangle$ and $\langle 1, 8 \rangle$, then find the magnitude and direction of the resultant vector. 2. **Add the vectors:** $$\langle 7, -2 \rangle + \langle 1, 8 \rangle = \langle 7+1, -2+8 \rangle = \langle 8, 6 \rangle$$ 3. **Find the magnitude of the resultant vector:** The magnitude formula is $$|\mathbf{v}| = \sqrt{x^2 + y^2}$$ So, $$|\langle 8, 6 \rangle| = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10$$ 4. **Find the direction (angle) of the resultant vector:** The direction $\theta$ is given by $$\theta = \tan^{-1}\left(\frac{y}{x}\right) = \tan^{-1}\left(\frac{6}{8}\right)$$ Calculate: $$\theta = \tan^{-1}(0.75) \approx 36.87^\circ$$ Rounded to the nearest degree: $$\theta \approx 37^\circ$$ 5. **Interpretation:** The resultant vector has magnitude 10 and points at an angle of $37^\circ$ above the positive x-axis (east direction). **Final answer:** - Sum vector: $\langle 8, 6 \rangle$ - Magnitude: 10 - Direction: $37^\circ$