Discussion in 'Physics' started by braddy, Sep 4, 2005.

  1. braddy

    Thread Starter Well-Known Member

    Dec 29, 2004
    hi ,

    I have a problem about vector coordinates. this is the problem:

    We have a 2-dimension space [x(unit vector i) and y( unit vector j)].

    I have a circle of center 0 (0,0) and a point P such that OP = r.

    Vector OP and the x-axis have an angle of θ .

    there is a unit vector ir , with the same direction with OP( but starting at P.)

    Another unit vector it starts at P , but vector it is perpendicular to vector ir. (vector it 's direction is toward north-west)

    Express vector ir as a combination of unit vectors i and j.

    Express vector it as a combination of unit vectors i and j.

    I found that ir = cos(θ ) i + sin(θ ) j

    how to find it ? when I try to compute for vector it, I found the same as vector ir, but I am not sure.

    Please help

    Thank you
  2. Nirvana

    Well-Known Member

    Jan 18, 2005
    Hi there im not quite clear on what is being asked but to state a vector in terms of its components you need to do the following.

    Let x -axis be the i component and y - axis be j component.
    Look on your graph and see where the tip of the vector touches in terms of its coordinates ( x,y), now the value of x say it was 2 you would write 2i, then say the y axis coordinate was 3 you would write 3j, putting it together you would write that your vector with it's magnitude and direction is equal to 2i +3j.
  3. Fahad khan

    New Member

    Sep 26, 2006
    Hi there, As the unit vector it is perpendicular to the unit vector ir so its

    angle with the x-axis is 90+theta.Substituting this value in expression for ir we get


    or it =-cos(theta)i+sin(theta)j

    As cos(90+theta)=-cos(theta) and sin(90+theta)=sin(theta).

    I hope this solves your problem.
    Thank you