1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Vectors ; specifically cross product application

  1. Sep 6, 2010 #1
    1. The problem statement, all variables and given/known data

    vector A = 1.5i + 6.7j - 7.4k
    vector B= -8.2i + 6.5j + 2.3k

    (f) What is the magnitude of the component of vector A perpendicular to the direction of vector B but in the plane of vector A and B.

    3. The attempt at a solution

    This part of the problem has me kinda stumped. My attempt at the solution was using the application of the cross product : C = ABsin(theta).

    I calculated the angle between the two as 82.43 degrees, and realized that this formula gave me the same thing as simply taking the magnitude of the cross product vector which I calculated to be 107.207.

    This shows me that my fundamental approach to this problem is incorrect, but I have no idea where to go with it. Any pointers would be appreciated.
  2. jcsd
  3. Sep 6, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    Magnitudes of vectors isn't all you need, you also need directions. It would be nice to find a vector that is perpendicular to B but in the plane of A and B, right? Then you could just find the magnitude of A along that direction. How about (AxB)xB? Can you see why that works?
  4. Sep 6, 2010 #3
    Looking at a graph of AxB, I think I can see why that (AxB)xB would give me a vector perpendicular to B in the plane, and I'd just have to apply the dot product to get the component of A in the direction of B.
  5. Sep 6, 2010 #4


    User Avatar
    Science Advisor
    Homework Helper

    Sure. (AxB)xB is perpendicular to B, and it's also perpendicular to AxB which is the normal to plane containing A and B. And, yes, from here you can use a dot product.
  6. Sep 6, 2010 #5
    I successfully solved this problem, thanks for the nudge in the right direction.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Vectors specifically cross Date
Specific heat Friday at 1:42 AM
Inelastic 2D Collision with Vector Components Feb 26, 2018
How does this solution make any sense? (Tension problem) Feb 25, 2018
Physics Vector Problem Feb 25, 2018
Hyperplanes and distance Feb 21, 2018