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=(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...