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Homework Help: Finding a unit vector.

  1. Jan 30, 2012 #1
    Find the unit vector that makes an angle θ=-3∏/4 with the positive x-axis




    I know to find a unit vector you divide the given vector by its magnitude, so I guess my problem is finding any vector that makes that angle with the positive x axis. I figured if that angle was the slope of a line, then when x=1, y=-3∏/4. So I divided the vector <1,-3∏/4> by its magnitude and got the wrong answer. Could someone point me in the right direction?

    Thanks in advance.
     
  2. jcsd
  3. Jan 30, 2012 #2

    Char. Limit

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    Gold Member

    Well, first, y is not 3pi/4. Remember your equation for slope: tan(theta) = y/x. What's tan(theta) in this case? That'll give you y/x = c for some c, and you can use THAT to get a vector.
     
  4. Jan 30, 2012 #3

    HallsofIvy

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    Science Advisor

    A unit vector that makes angle [itex]\theta[/itex] with the positive x-axis is [itex]cos(\theta)\vec{i}+ sin(\theta)\vec{j}[/itex]. I thought everyone knew tha!

    "I figured if that angle was the slope of a line"
    No, the tangent of the angle is the slope of the line.
     
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