Question

Find the magnitude and direction of the vector. Round the length to the nearest tenth and the degree to the nearest unit. Diagram is not drawn to scale.

Answer 1

Refer to the diagram shown below.

The vector has a magnitude of a and a direction of θ degrees south of west.

Use the Pythagorean Theorem to calculate a.
a² = (-530)² + (-200)² = 320900
a = √(320900) = 566.48 mi ≈ 566.5 mi

By definition,
tan θ = (-200)/(-530) = 0.3774
θ = tan⁻¹ 0.3774 = 20.68° ≈ 21°

Answer: about 566.5 mi; 21° south of west.