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)?

Respuesta :

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

From the given info, we have

[tex]\|\vec u\|=\sqrt{{u_1}^2+{u_2}^2}=3.15[/tex]

[tex]\tan\theta_{\vec u}=\tan313^\circ=\dfrac{u_2}{u_1}[/tex]

[tex]\implies u_1\approx2.14,u_2\approx-2.30[/tex]

and

[tex]\|\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}[/tex]

[tex]\implies v_1\approx0.956,v_2\approx3.34[/tex]

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