Question

Find the magnitude and direction of the vector represented by each of the following pairs of components:

(a) 𝐴𝑥 = 3.0 𝑐𝑚, 𝐴𝑦 = −4.0 𝑐𝑚;

(b) 𝐴𝑥 = −5.0 𝑚, 𝐴𝑦 = −12.0 𝑚;

(c) 𝐴𝑥 = −2.0 𝑘𝑚, 𝐴𝑦 = 3.0 𝑘𝑚.

Answer 1

$$A=\sqrt{A_x^2+A_y^2}$$

$$\theta=\tan^{-1}\frac{A_y}{A_x}$$

(a)

$$A=\sqrt{(3.0)^2+(-4.0)^2}=5.0\:\rm cm$$

$$\theta=\tan^{-1}\frac{-4.0}{3.0}=307^\circ$$

(b)

$$A=\sqrt{(-5.0)^2+(-12.0)^2}=13\:\rm m$$

$$\theta=\tan^{-1}\frac{-12.0}{-5.0}=247^\circ$$

(c)

$$A=\sqrt{(-2.0)^2+(3.0)^2}=3.6\:\rm km$$

$$\theta=\tan^{-1}\frac{3.0}{-2.0}=124^\circ$$