Finding A Vector with a specific angle

Question

How do you find the vector of length 2 in ℝ2 making an angle of 30∘ with the x-axis?

score 1 · Answer 1 · answered Mar 02 '15 at 00:20

1

say (x,y) is the vector you are looking for. it have to fulfill both:

then just solve the system

answered Mar 02 '15 at 00:20

avim

1

I'm not sure how to, can you please add a more detailed example. – user220283 Mar 02 '15 at 00:26
1

as @Famous Blue Raincoat said, see: http://math.stackexchange.com/a/149435/156457 Ask if it still not clear – avim Mar 02 '15 at 00:29

score 1 · Answer 2 · answered Mar 02 '15 at 01:14

$|v| = 2 \Rightarrow v = 2(\cos t, \sin t)$

$i = (1,0)$

$v \cdot (± i) = |v| \cdot |±i| \cdot \cos 30°$

$2(\cos t, \sin t) \cdot (±1, 0) = 2 \cdot 1 \cdot \frac{\sqrt{3}}{2}$

$± \cos t + 0 = \frac{\sqrt{3}}{2}$

$\cos t = ± \frac{\sqrt{3}}{2}$

$\cos^2t + \sin^2t = 1$

$\sin t = ± 1 / 2$

There are four vectors. [++], [+-], [-+], [--]

2 Answers2