Help with vectors: how do I solve this?

Question

See attached picture link. I'm doing an online physics course, and I'm not grasping the explanation given in the video lecture. I would appreciate if someone could tell me how to solve the problem rather than just giving me the solution.

Thanks in advance.

http://i5.photobucket.com/albums/y182/Musician101/vector_zps95071524.png

godzyx · Accepted Answer

You have magnitude of vector a, | a | = 7. So you know vector is oriented 55° from x-axis. So if we make x-axis our reference, the angle will be -55°.

So you are looking for <x, y, z>. But you do not have enough info to work out three numbers, this means one is 0. Typically, angle corresponds to x and y planes, so z-component = 0.

Now this is just right triangles and basic trig (sin/cos).

x-component uses magnitude and cos of angle. y-component uses magnitude and sin.

<4.02, -5.73, 0>

Edit. Yes, x-component is 7 cos 55°.

Your calculator has to be in degree mode. As for my answers not being correct, there are a number of distinct possibilities.

Significant figures. I have 3. This has an effect on automated homework systems.

Planes. I made an assumption based on 55 clockwise from x-axis. This could be wrong. I made the z-coordinate 0. With the information provided, I believe I am correct.

- x axis. I read this as x axis. But the -x axis is 180°. So 55° CW from -x axis is 180° - 55° = 125°

7 cos 125° = -4.02

7 sin 125° = 5.73

Try:

<-4.02, 5.73, 0>

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Help with vectors: how do I solve this?

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