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Another i j k vectors question.

  1. Oct 29, 2015 #1
    Hi everyone. Aftrer doing a search I found loads of information but I still cant get my head around these damm vectors. I understand the basics and how to work out the dot product if given the question in a given way.

    An example of the questions im being asked are:

    The following two vectors are:
    p = 4i + 3j - 2k and q = 2i - 4j - 3k
    i) Find p+ q
    ii) Find p – q
    iii) Find the scalar product of pq
    iv) Find the direction cosines for both p and q
    v) Find the angle between vectors p and q, giving your answer to 2 decimal places (d.p.)

    When the vectors are written in this form I literally dont know where to start!

    Any help would be much appreciated.
  2. jcsd
  3. Oct 29, 2015 #2


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    Staff: Mentor

    In what way do you understand?
  4. Oct 29, 2015 #3
    By using the (a)(b)cos0 rule.

    To use this I would need to know what a b and the angle would be. So if its drawn for me (almost like a tri angle) its straight forward. I take it the "i j k" must refer to "a b 0"?

    Sorry if im miles out this is all totally new to me!
  5. Oct 29, 2015 #4


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    Staff: Mentor

    No. i, j, and k are unit vectors (vectors of length 1), pointing along the x, y, and z axes, respectively. Take p, for instance. You have
    \mathbf{p} = 4 \mathbf{i} + 3 \mathbf{j} - 2 \mathbf{k} = 4 \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix} + 3 \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix} -2 \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} = \begin{pmatrix} 4 \\ 3 \\ -2 \end{pmatrix}
    which represents a vector with its origin at ##(x,y,z) = (0,0,0)## and its tip at ##(4,3,-2)##.

    You will need to get your hands on a good book on linear algebra. I don't know much about web resources, but there is a very basic introduction on Math is Fun. You can also have a look at Khan Academy.
  6. Oct 29, 2015 #5
    Brilliant thats extremely helpful.

  7. Oct 29, 2015 #6


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    Staff Emeritus
    Science Advisor

    (a, b, c)+ (p, q, r)= (a+ p, b+ q, c+ r).

    And the scalar product is (a, b, c).(p, q, r)= ap+ bq+ cr
  8. Oct 29, 2015 #7


    Staff: Mentor

    Thread moved out of homework sections, as this question is not specifically a homework question.
  9. Oct 30, 2015 #8
    Sorry, im a noob!

    For anybody else looking for help on this subject I found this website very helpful.. http://www.mathtutor.ac.uk/
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