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Is this all correct? (more bl dy vectors!)

  1. Mar 6, 2008 #1
    Is this all correct? (more bl**dy vectors!)

    I hope these are right, but I have the nagging suspicion that they're not? Where have I gone wrong (if I have indeed gone wrong)?
    1. The problem statement, all variables and given/known data
    line P has equation (x+3)/2 = y = z-1
    (a) Show that point Q (2,1,2) does not lie on line P.
    (b) Write down the parametric equations for the line.
    (c) Use dot product properties to find the co-ords of point R which is on P, such that QR is perpendicular to P.


    3. The attempt at a solution
    (a) sub (2,1,2) into the equation:
    (2+3)/2 = 1 = 2-1
    5/2 = 1 = 1
    they don't equal, therefore point Q does not lie on line P.
    Is it that simple, or do I need to use [v(P) = (-3,0,1) + t(2,1,1)] and the parametric equations such that x=2t-3=2, y=t=1 & z=t+1=2 and attempt a solution. Here it is inconsistent.

    (b) parametric equations:
    x=2t-3
    y=t
    z=t-1

    (c) dot product:
    let u = (2,1,2) and v=(-3,0,1)
    u.v = (2 1 2).(-3 0 1) |i 2 -3 |
    = det |j 1 0 | = i - 8j + 3k
    |k 2 1 |
    point R = (1, -8, 3).
    again, I feel I've skipped a step here, but it's 11.30pm and I'm too tired to think any further!

    many thanks in advance! I'll be checking again in the am.
     
  2. jcsd
  3. Mar 6, 2008 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, it really is that simple!


     
  4. Mar 6, 2008 #3
    thanks alot for that.
    I have this problem of always thinking the solution has to be more complex than it appears to be!
    I really must go out and buy another Occam's razor. Mine's obviously too blunt and ain't working as well as it should.
     
  5. Mar 6, 2008 #4
    very minor quibble here: shouldn't that 4/3 be 5/3 ? :wink:
     
  6. Mar 7, 2008 #5

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Yes, of course it should.
     
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