Linear Algebra

  • Thread starter gunnar
  • Start date
  • #1
gunnar
40
0
There are two vectors (1,0,-1) and (0,1,1)
I need to find all the unit vectors x in R3 that make an angle of pi/3 with each of the vectors above.

Can someone please help with this problem?
 

Answers and Replies

  • #2
vincentchan
609
0
hint:
use dot product to find the angle between vectors
 
  • #3
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,967
19
You should be able to use the three constraints on your solution vector (unit vector, specified angle with a vector, specified angle with another vector) to write down three equations in the components of your solution vector. Then, solve.
 
  • #4
gunnar
40
0
O.K I figured out that the angle between the given vectors is 60 degrees or pi/3

The angle between the unit vectors and each of the given vectors is supposed to be pi/3 also. So I used the dot product to calculate

c=sqrt(2) since the unitvector has length 1 and both the given vectors have the length sqrt(2)

Don't seem to be able to get the right answear.
The correct answear is (1/sqrt(2), 1/sqrt(2), 0) only one vector.

How to reach that conclusion I have no idea
 
  • #5
da_willem
599
1
Lets call the components of the vector you seek (a,b,c). Now there are three restriction on these three numbers. So when you write down the tree restrictions Hurkyl gave in terms of a,b and c you have three equations with three unknowns which you can solve. Can you translate the restrictions from words to algebra?
 

Suggested for: Linear Algebra

Replies
14
Views
192
Replies
3
Views
314
Replies
1
Views
626
  • Last Post
Replies
31
Views
2K
Replies
4
Views
368
Replies
3
Views
572
Replies
5
Views
426
  • Last Post
Replies
20
Views
506
Replies
1
Views
276
Top