Question

required information
four vectors are shown below, where ( l = 8.00 ).

find the ( x )-component of the vector ( vec{c} ).

(square) m

Explanation:

Step1: Identify vector direction

Vector $\vec{C}$ makes $20.0^\circ$ with the negative y-axis, so its angle from positive x-axis is $90.0^\circ + 20.0^\circ = 110.0^\circ$.

Step2: Calculate x-component

Use $C_x = l\cos\theta$, substitute $l=8.00$, $\theta=110.0^\circ$.
$C_x = 8.00 \times \cos(110.0^\circ)$
$\cos(110.0^\circ) = \cos(90^\circ+20^\circ) = -\sin(20^\circ) \approx -0.3420$
$C_x = 8.00 \times (-0.3420) = -2.736$

Answer:

$-2.74$ m (rounded to three significant figures)