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5 votes
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)?

User Gustash
by
8.3k points

1 Answer

3 votes

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=(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]</p><p>[tex]\tan\theta_(\vec v)=\tan79.0^\circ=(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...

User Bruno Kinast
by
8.9k points
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