# Vectors in a 3D plane

OK so I am a bit confused. I am doing multiplication of vectors. I am a bit confused about the angles between two vectors. Lets say a(vect)=(3.0)i-(4.0)j; b(vect)=(2.0)j+(3.0)k in unit vector notation. Or generally how are angles between two vectors in 3d defined. Not just in terms of the dot or cross equ.

Is it about the definition of the angle between two vectors?

Or is it about finding the angle between two vectors given their components?

SteamKing
Staff Emeritus
Homework Helper
AFAIK, dot and cross products are how angles between vectors are determined, esp. in 3D. It's not like you are going to slap a protractor on them and read off the angle.

jtbell
Mentor
Conceptually, the angle between two vectors is what you get if you put them together tail to tail and use a protractor to measure the angle that this forms. Calculationally, if you have the components of both vectors as in your example, equate the two common formulas for the dot product and solve for the angle:

$$A_x B_x + A_y B_y + A_z B_z = |\vec A||\vec B| \cos \theta$$

Never mind I misread something earlier. Making my question very illogical. Sorry. Thanks though.

Last edited:
Nugatory
Mentor
I know how to find the angle between vectors. I know theta is ~110 just don't know where the ~110 deg comes from. By this I mean how is that angle defined. I just do not know how angle between vectors in a 3d plane are defined.

Conceptually, you put the two vectors together tail to tail as jtbell says above. The two vectors will lie in a single two-dimensional plane (which may be slanted/tilting); in that two-dimensional plane you can use a protractor to find the angle just as you would if you had started with vectors in only two dimensions.