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Angle: vector (a + b)

  1. Oct 8, 2011 #1
    1. The problem statement, all variables and given/known data

    if vector :

    line a starts from co-ordinates (0,0) and ends at (5,3)

    line b starts from co-ordinates (0,0) and ends at (1,2)

    what angle to the x-axis does the vector (a + b) make?

    2. Relevant equations

    tan ∅ = opposite / adjacent

    3. The attempt at a solution

    we can work out what angle a makes then what angle b makes.

    then subtract angle b from a.

    tan a = opposite / adjacent
    tan a ^-1 (3/5) = a=30.964

    tab b ^ (2/1) =b=63.435

    b-a = 63.435-30.964
    = 32.47 degrees

    is this correct?
     
  2. jcsd
  3. Oct 8, 2011 #2

    gb7nash

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    No. You want to add the vectors first, then take the angle. What is the x component of a+b? What is the y component of a+b? Once you have these, then you can use the angle formula.
     
  4. Oct 8, 2011 #3
    (5,3) + (1,2) = (6,5) is the vector of (a+b)

    tan a = opposite / adjacent
    tan a ^-1 (5/6) = a=39.806 degrees

    tan x ^-1 (3/5) = x=30.964

    angle of (a+b) = 8.842 degrees

    is this correct
     
  5. Oct 8, 2011 #4

    gb7nash

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    This is fine. I'm not quite sure why you're still subtracting angles though.

    tan(angle of a+b) = opposite/adjacent = ...

    What's opposite? adjacent?
     
  6. Oct 8, 2011 #5
    tan a = opposite / adjacent
    tan a ^-1 (5/6) = a=39.806 degrees
     
  7. Oct 8, 2011 #6

    gb7nash

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    This is the correct answer. Minor technicality though. You're taking the tangent of the angle of a+b, not the tangent of a.
     
  8. Oct 8, 2011 #7
    tan ( a + B ) = opposite / adjacent
    tan (a+b) ^-1 (5/6) =

    angle of (a + b)=39.806 degrees

    Thanks gb7nash
     
  9. Oct 8, 2011 #8

    Mark44

    Staff: Mentor

    I have no idea what you mean by this.
     
  10. Oct 8, 2011 #9

    gb7nash

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    Good catch, I didn't even notice that.
     
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