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Norma-Jean [14]
3 years ago
9

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)?
Mathematics
1 answer:
krek1111 [17]3 years ago
6 0

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...

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