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If $ v $ lies in the first quadrant and makes an angle $ \frac{\pi}{3} $ with the positive x-axis and $ \mid v \mid = 4 $, find $ v $ in component form.

$$

v=<2,2 \sqrt{3}>

$$

Vectors

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Missouri State University

Campbell University

Baylor University

Boston College

So for the given problem, If v lies in the first quadrant and makes an angle of pi over three with the positive X. Axis and the magnitude of the is four, we want to find V. In component form. So one way we could look at this is recognizing that pi over three because degrees. So how we're going to look at this is we could do um V the magnitude times code sign. What are vector is going to look like? Is V co Cynthia to the sign painter because we're creating a right triangle. Um and if we do this, we'll be able to see that there's going to be an X. Component, that's vico, santa, ana Y component, that's be signed data. So what we're gonna end up having is four times co sign of 60 that's going to give us to And then four times co sign Are four times seven or 60 that's going to give us to route three.

California Baptist University

Vectors