How Do I Find Unit Vectors Perpendicular to Given Vectors?

[Pogorz]

Homework Statement

My prof gave me a homework assignment and i don't really understand how to do the question.

You are give two vectors \vec{A}=(3,1,-3) and\vec{B}=(-2,3,4)
a) Find the angle between the two vectors
b) Find all the unit vectors (if there are more than one) perpendicular to both vectors.

Homework Equations

\vec{A}x\vec{B}=(A_{y}B_{z}-A_{z}B_{y})\hat{i}-etc(don't feel like typing it all out, you guys know what i mean)

The Attempt at a Solution

I drew out graphs (sort of) of the vectors to get a grasp on it. I'm not sure what it's asking for in part b) of the question. And I have NO idea how to find the angles between the lines.

 

[gabbagabbahey]

Hint: \textbf{A}\cdot\textbf{B}=|\textbf{A}||\textbf{B}|\cos\theta...

 

[Pogorz]

Hint: \textbf{A}\cdot\textbf{B}=|\textbf{A}||\textbf{B}|\cos\theta...

just to see if I'm on the right path... (Ax)(Bx) = i, (Ay)(By) = j, (Az)(Bz) = k. i+j+k = \textbf{A}\cdot\textbf{B}?

My calc teacher in high school never did matrices with us, and neither did my phys 30 teacher, first week on uni and my prof expects me to know it so I'm getting the lovely people of the internet to teach me. Does anyone have a site with vector problems that would help me strengthen these skills?

 

[gabbagabbahey]

I think you'd better spend a little while studying (either from your textbook, or from a site like http://emweb.unl.edu/Math/mathweb/vectors/vectors.html ) before attempting any problems.

 

[Pogorz]

Okay, read through unit vectors in my physics textbook. and my calc textbook. and on that site gabba posted. and my class notes. and i still don't understand what part b) is asking me to do.

 

[rock.freak667]

Okay, read through unit vectors in my physics textbook. and my calc textbook. and on that site gabba posted. and my class notes. and i still don't understand what part b) is asking me to do.

look at the "cross product" section of the given link

 

[gabbagabbahey]

Well, \textbf{A}\times\textbf{B} will always produce a vector perpendicular to both \textbf{A} and \textbf{B} right?

 

[Pogorz]

Okay, thanks for the help. I got some answers that do make sense. And I'd just like to point out i have no experience of any 3D vectors before monday, and anything i do know i learned through my textbooks and the internet. So thanks for the patience.