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a displacement vector \\( \vec{r} \\) in the xy plane is 20.0 m long and directed at angle \\( \theta = 21.0^\circ \\) in the figure. determine (a) the x component and (b) the y component of the vector.
(a) number
units
(b) number
units
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Explanation:

Step1: Calculate x-component

The x-component of a vector is found using the cosine of the angle:
$r_x = r\cos\theta$
Substitute values: $r = 20.0\ \text{m}$, $\theta = 21.0^\circ$
$r_x = 20.0 \times \cos(21.0^\circ)$
$r_x \approx 20.0 \times 0.9336 = 18.672$

Step2: Calculate y-component

The y-component of a vector is found using the sine of the angle:
$r_y = r\sin\theta$
Substitute values: $r = 20.0\ \text{m}$, $\theta = 21.0^\circ$
$r_y = 20.0 \times \sin(21.0^\circ)$
$r_y \approx 20.0 \times 0.3584 = 7.168$

Answer:

(a) 18.7, Units: m
(b) 7.17, Units: m