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: Scalar product question

  1. Feb 13, 2005 #1
    Consider the two vectors M =(a,b) = ai+bj and N = (c,d) = ci +dj, where a =4, b =4, c = -1, and d = 1. a and c represent the x-displacment and b and d represent the y-displacment in a Cartesian xy co-ordinate system.
    Note: i and j represent unit vectors(i.e. vectors of length l)in the x and y directions, respectively. what is the value of the scalar product N x N?
  2. jcsd
  3. Feb 13, 2005 #2
    Do you know the definition of the scalar product? It's just the product of each i component + the product of each j component.
  4. Feb 13, 2005 #3
    but then wouldnt that be (4,-1)+(4,1) so you get (-3) +(5)
  5. Feb 13, 2005 #4
    Sorry I should have specified:

    If you have 2 vectors in the form ai + bj and ci + dj, you obtain the scalar product by multiplying a by c and b by d to obtain ac + bd. You multiply each component seperately before adding.
  6. Feb 13, 2005 #5
    I assume by (4, -1) you mean 4 x -1, but where did that -1 come from?

    You should also know that the scalar product, a.b = |a||b|cos theta, where theta is the angle between a and b. From that, you should be able to see what the scalar product of n with itself is.
  7. Feb 13, 2005 #6
    c=-1, so -4 + 4 =0 , so your saying i have to solve for the angle in betwwen first, which can be easily done?
  8. Feb 13, 2005 #7
    It's not necessary here but if you're ever given a question like "Magnitude of A is x and Magnitude of B is y and the angle between them is t degrees find A dot B" you know how to apply it.
  9. Feb 13, 2005 #8
    well zero isnt the answer
  10. Feb 13, 2005 #9
    Are you sure that's written correctly? It looks like it's asking you to take the dot product of a vector with itself. Additionally, N x M is usually the convention for the vector product (cross product). Can you confirm the question is worded exactly like in the quotes?
  11. Feb 13, 2005 #10
    yea on the homework the question is what is the value of the scalar product N <dot> N? is it a trick question or something
  12. Feb 13, 2005 #11
    It was a trick. Vector M is irrelevant. Just take the dot product of N with itself (-1*-1+1*1)
  13. Feb 13, 2005 #12
    correct thank you so much, but what if i do need M dot N
  14. Feb 14, 2005 #13
    Just multiply the i component of N and the i component of M together then sum it to the product of the j component of N and the j component of M
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook