3-dimensional vector

**Sputnik** · November 21st 2008, 10:49 PM

I'm having a bit of an issue understanding how to use vectors, and could use a little help with a basic one:
"Find a unit vector that makes equal angles with the three coordinate axes."

I don't want a complete solution, just a hint on where to start!

**earboth** · November 22nd 2008, 04:28 AM

Originally Posted by Sputnik

I'm having a bit of an issue understanding how to use vectors, and could use a little help with a basic one:
"Find a unit vector that makes equal angles with the three coordinate axes."

I don't want a complete solution, just a hint on where to start!

1. Draw a sketch (compare attachment)

2. Prove that your vector includes equal angles with the coordinate axes. Use:

If $\alpha$ is included by the vectors $\overrightarrow{ v_1}$ and $\overrightarrow{ v_2}$ then

$\cos(\alpha) = \dfrac{\overrightarrow{ v_1} \cdot \overrightarrow{ v_1}}{|\overrightarrow{ v_1}| \cdot |\overrightarrow{ v_1}|}$

(For your confirmation: $\alpha \approx 54.74^\circ$

3. Calculate the unit vector of your vector.

(for your confirmation: You must use $\sqrt{3}$ as a divisor)

**Sputnik** · November 22nd 2008, 12:20 PM

Haha, nr. 2 would have been enough, now I think I get it. Thanks for the assist!

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