Question

review the graph. which statement describes the equivalent vectors? the magnitudes are 10, and the direction angles are about 18°. the magnitudes are 10, and the direction angles are about 162°. the magnitudes are 100, and the direction angles are about 18°. the magnitudes are 100, and the direction angles are about 162°.

Explanation:

Step1: Calculate vector magnitude

For a vector with components \((x,y)\), magnitude \(r = \sqrt{x^{2}+y^{2}}\). Assume vector has components \((9, 3)\) (estimated from graph), \(r=\sqrt{9^{2}+3^{2}}=\sqrt{81 + 9}=\sqrt{90}\approx 10\).

Step2: Calculate direction - angle

\(\theta=\arctan(\frac{y}{x})\), with \(x = 9,y = 3\), \(\theta=\arctan(\frac{3}{9})=\arctan(\frac{1}{3})\approx18^{\circ}\).

Answer:

The magnitudes are 10, and the direction angles are about 18°.