1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Vector question (scalar products)

  1. Feb 9, 2009 #1
    Find scalars s, t s.t. C - sA - tB is perpendicular to A and B

    A = i + j + 2k
    B = 2i - j + k
    C = 2i - j + 4k

    I took the cross product of A and B
    (1, 1, 2) x (2, -1, 1) =
    |i j k|
    |1 1 2|
    |2 -1 1|
    = 3i + 3j - 3k

    OK, that should be perpendicular to both vectors A and B I'm guessing...
    But how do I still determine the scalars s and t -- there is only one equation!
  2. jcsd
  3. Feb 9, 2009 #2


    User Avatar
    Gold Member

    Ill let Q = C - sA - tB.

    If Q is perpendicular to both A and B, and the vector (3,3,-3) is also perpendicular to both A and B (as you have calculated), then it should follow that Q is a scalar multiple of (3,3,-3) right?

    k(3,3,-3) = Q

    Now you have a system of 3 equations in 3 variables (s,t,k).


    Another way that you could solve it would be to realise that you need to find s,t such that Q.A = Q.B = 0 (a zero scalar product implies orthogonality), and form a system of two equations in two variables (s,t).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook