I don't understand unit vectors

In summary, the homework asks for you to find the angle between two vectors, and find all the unit vectors perpendicular to those vectors.
  • #1
Pogorz
15
0

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 [tex]\vec{A}[/tex]=(3,1,-3) and[tex]\vec{B}[/tex]=(-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



[tex]\vec{A}[/tex]x[tex]\vec{B}[/tex]=(A[tex]_{y}[/tex]B[tex]_{z}[/tex]-A[tex]_{z}[/tex]B[tex]_{y}[/tex])[tex]\hat{i}[/tex]-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.
 
Physics news on Phys.org
  • #2
Hint: [itex]\textbf{A}\cdot\textbf{B}=|\textbf{A}||\textbf{B}|\cos\theta[/itex]...
 
  • #3
gabbagabbahey said:
Hint: [itex]\textbf{A}\cdot\textbf{B}=|\textbf{A}||\textbf{B}|\cos\theta[/itex]...

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

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?
 
  • #5
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.
 
  • #6
Pogorz@gmail. said:
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
 
  • #7
Well, [itex]\textbf{A}\times\textbf{B}[/itex] will always produce a vector perpendicular to both [itex]\textbf{A}[/itex] and [itex]\textbf{B}[/itex] right?
 
  • #8
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.
 

What is a unit vector?

A unit vector is a vector that has a magnitude of 1 and is used to represent direction or orientation in a coordinate system.

Why are unit vectors important?

Unit vectors are important because they allow us to describe and understand the direction and orientation of vectors without being affected by their magnitude.

How do you find the unit vector of a given vector?

To find the unit vector of a given vector, divide the vector by its magnitude. This will result in a vector with the same direction, but a magnitude of 1.

What is the difference between a unit vector and a normal vector?

A unit vector has a magnitude of 1, while a normal vector can have any magnitude. Unit vectors are commonly used for direction and orientation, while normal vectors are used for perpendicularity and distance calculations.

Can unit vectors be negative?

Yes, unit vectors can be negative. The negative sign simply indicates the direction of the vector.

Similar threads

  • Advanced Physics Homework Help
Replies
5
Views
1K
  • Advanced Physics Homework Help
Replies
5
Views
2K
  • Linear and Abstract Algebra
Replies
14
Views
497
  • Precalculus Mathematics Homework Help
Replies
20
Views
676
  • Advanced Physics Homework Help
Replies
2
Views
2K
  • Linear and Abstract Algebra
Replies
3
Views
184
  • Calculus and Beyond Homework Help
Replies
13
Views
1K
Replies
1
Views
868
  • Calculus and Beyond Homework Help
Replies
8
Views
925
Replies
2
Views
200
Back
Top