1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear combination problem

  1. Jan 14, 2009 #1
    1. The problem statement, all variables and given/known data

    Under what restrictions on c,d,e will the combinations c*u+d*v+e*w fill in the dashed triangle?

    2. Relevant equations

    3. The attempt at a solution

    I think c,d,e>=0 and bcos the triangle it's in a plane maybe remove one of c,d or e doing c+d+e=number?

    Attached Files:

  2. jcsd
  3. Jan 19, 2009 #2
    The midpoint between u and v is (u + v)/2. Convince yourself by drawing a parallelogram. This fact can be used to find conditions on c, d such that the linear combinations cu + dv fill in the line segment between u and v.

    A better way to think about this: The vector from u to v is v - u. Starting at u, we can vary the length of v - u to fill in the line segment. Consider u + t(v - u) for t in [0, 1].

    To fill in the entire triangle including its inside, use the same sort of reasoning: Starting at u, we can vary the lengths of v - u and w - u under certain restrictions.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Linear combination problem
  1. Linear combinations (Replies: 11)

  2. Linear combination (Replies: 5)

  3. Combination Problem (Replies: 3)

  4. COmbination problem (Replies: 7)

  5. Combinations problem (Replies: 9)