Find Direction Angle of Vector in Plane

[htk]

can anyone please help me how to find the direction angle of a vector? Thank you!

 

[Dragonfall]

Think about the triangle that the vector and its components form.

 

[HallsofIvy]

can anyone please help me how to find the direction angle of a vector? Thank you!

I presume you are talking about vectors in the plane since vectors in three dimensions have three "direction angles". How are you given the vector? If in x,y components, say ai+ bj, then b/a is the tangent of the angle the vector makes with the x-axis:
\theta= arctan(\frac{a}{b}).

 

[tiny-tim]

Welcome to PF!

Hi htk! Welcome to PF!

can anyone please help me how to find the direction angle of a vector? Thank you!

You find the cosine of the angle …

which you do by finding the dot product. ​

 

[HallsofIvy]

Hi htk! Welcome to PF!


You find the cosine of the angle …

which you do by finding the dot product. ​

His question was about a single vector. What do you want him to take the dot product with?

 

[tiny-tim]

… just answering the question as asked! …

His question was about a single vector. What do you want him to take the dot product with?

with whatever mysterious entity he had in mind when he specified …

can anyone please help me how to find the direction angle of a vector?

 

[Elucidus]

A two-dimensional vector \langle a,b \rangle will have a direction angle \theta \text{ such that } \tan \theta = b / a (not (a/b)) but this does not uniquely determine \theta, even if it is restricted to the interval [0, 2 \pi ).

You also need to consider in which quadrant does the vector lie. You need to adjust the value of \theta so that it falls into the correct quadrant.

For example, the vector \langle -3, 3 \rangle has a direction angle so that \tan \theta = 3 / -3 = -1 \text{ which implies } \theta = -\pi /4 + n \pi for an appropriate choince of integer n. Since the vector is in the second quadrant, we need to select the angle to fall there, so \theta = 3\pi / 4 (here n = 1).

I hope this helps.

--Elucidus

 

[Dragonfall]

His question was about a single vector. What do you want him to take the dot product with?

I suppose he could dot it with (1,0).

EDIT: Modulo sign.