Question

Two vectors, and lie in the xy plane. Their magnitudes are 3.15 and 3.47 units, respectively, and their directions are 313 n 79.0, respectively, as measured counterclockwise from the positive x axis. What are the values of (a) and (b)?

Answer 1

Let $\vec u=(u_1,u_2)$ and $\vec v=(v_1,v_2)$ be the two given vectors, with magnitude $\|\vec u\|$ and $\|\vec v\|$ and directions $\theta_{\vec u}$ and $\theta_{\vec v}$, respectively.

From the given info, we have

$\|\vec u\|=\sqrt{{u_1}^2+{u_2}^2}=3.15$

$\tan\theta_{\vec u}=\tan313^\circ=\dfrac{u_2}{u_1}$

$\implies u_1\approx2.14,u_2\approx-2.30$

and

$\|\vec v\|=\sqrt{{v_1}^2+{v_2}^2}=3.47[/tx][tex]\tan\theta_{\vec v}=\tan79.0^\circ=\dfrac{v_2}{v_1}$

$\implies v_1\approx0.956,v_2\approx3.34$

No telling what the "values of (a) and (b)" is referring to, so I'll leave the rest to you...