Question

a vector has an x-component of -2.5 meters and a y-component of 4.2 meters. Express the vector in magnitude angle form.

Answer 1

Let the vector $\bf a$ has components

$a_x=-2.5\:\rm m$

$a_y=4.2\:\rm m$

Thus, the magnitude of the vector $\bf a$

$$a=\sqrt{a_x^2+a_y^2}=\sqrt{(-2.5)^2+4.2^2}=4.9\:\rm m$$

The angle that vector $\bf a$ makes with positive x-direction

$$\theta=\tan^{-1}\frac{a_y}{a_x}=\tan^{-1}\frac{4.2}{-2.5}=121^{\circ}$$

Answer: ${\bf a}=(4.9\:\rm m;121^{\circ})$