Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Vector Help

  1. May 20, 2006 #1
    Hello, I have a quick question that I think seems stupid but I can't find an answer for it. It's about vectors in a mechanics module. Anyhow, this is the question:

    Determine p and q:

    p(4i + 3j) + q(12i + 5j) = 68i + 33j, where p and q are contants.

    I can only think to do this by trial and error to get p = 3.5 and q = 4.5. Is there a proper method to work out something like this?
  2. jcsd
  3. May 20, 2006 #2
    Yes there is.

    If the components (i and j in this case) of two vectors are equal, then the two vectors are equal. So, in your equation, you need the components on one side to be equal to the components on the other side. This should give you two linear equations, which I am going to assume you can solve.
  4. May 20, 2006 #3


    User Avatar
    Science Advisor
    Homework Helper

    [tex]p(4\mathbf{i} + 3\mathbf{j}) + q(12\mathbf{i} + 5\mathbf{j}) = 68\mathbf{i} + 33\mathbf{j}[/tex]

    [tex](4p + 12q)\mathbf{i} + (3p + 5q)\mathbf{j} = 68\mathbf{i} + 33\mathbf{j}[/tex]

    [tex]4p + 12q = 68\ \mbox{ and }\ 3p + 5q = 33[/tex]

    [tex]\left (\begin{array}{cc}4 & 12\\ 3 & 5\end{array}\right )\left (\begin{array}{c}p\\ q\end{array}\right ) = \left (\begin{array}{c}68\\ 33\end{array}\right )[/tex]

    [tex]\left (\begin{array}{c}p\\ q\end{array}\right ) = \left (\begin{array}{cc}4 & 12\\ 3 & 5\end{array}\right )^{-1}\left (\begin{array}{c}68\\ 33\end{array}\right )[/tex]
  5. May 21, 2006 #4
    Ah, thankyou. It was quite simple really :blushing:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook