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Dot product and cross product evaluation questions

  1. Jan 19, 2010 #1
    This question has a few parts.

    r = i + 2j + 3k
    s = 2i - 2j - 5k
    t = i - 3j - k

    Evaluate:

    a)(r.t)s - (s.t)r
    b)(r x s) x t.

    deduce that (r.t)s - (s.t)r = (r x s) x t


    can you prove this relative true for any three vectors

    a)(r.t)s - (s.t)r
    (r.t)s

    well I don't know what s is doing to inside the bracket. I don't think it's the cross product rule.
    Anyhow

    (r.t) means use dotty dot product

    r.t = |r||t|cos(x)

    problem uno. I don't know the angle between the vectors.

    Am I just being stupid. I thought about possibly trying to get the angle from the cross product, or using some trig identity but I think that'll be a road to nowhere

    Hint?

    Thanks
    Thomas
     
  2. jcsd
  3. Jan 19, 2010 #2
    hi,

    ok, first you need: (a) (r.t)s - (s.t)r

    you are given the vectors. For this, you dont need to use the formula:
    r.t = |r||t|cos(x)

    If you have two vector, do you know how to evaluate the dot/scalar product?
     
  4. Jan 19, 2010 #3
    im being an idiot

    r.t = (i - 6j- 3k)

    but what operation does the s outside of (r.t)s do?

    Thanks
     
  5. Jan 19, 2010 #4
    and im being an idiot agin, the dot product is scalar and so I'm merely multiplying all values of s by the scalar value returns from r.t

    1 - 6 - 3 = -8

    so (r.t)s = -8(s)

    => s = 16i - 16j - 40k

    Good so far?
     
  6. Jan 19, 2010 #5
    ya, good so far :)

    now, do the same for (s.t)r

    so can you now evaluate (a) (r.t)s - (s.t)r
     
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