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Tests of vectors/scalars

  1. Jul 30, 2009 #1
    groups: Vectors / Scalars / dosen't make sense
    Which of these groups do the following belong too

    1: a.b + b.c
    2: a+(a.b)
    3: (b.b)b+a
    4: (a.b)(b.c)
    5: (a.b).c

    a.b + b.c is adding the dot product of two vectors, then adding them so a Scalar for the final

    a+(a.b) is adding a vector to a product of two vectors so dosen't make sense e.g (1,1,1)+5

    (b.b)b+a also dosen't make sense, since it is the dot product of a vector added with two added vectors e.g (b*b=5)*(2,1,0)+(1,1,1)

    (a.b)(b.c) makes sense, and is a scalar, because the two dot products produce scalars which are then multiplied by each other

    (a.b).c is a vector because you get a scalar from a.b then multiply each component of C to create a new vector

    -

    hoping someone could check for me XD thanks
     
    Last edited: Jul 30, 2009
  2. jcsd
  3. Jul 30, 2009 #2
    really not sure about

    (b.b)*(a+b)

    i know a*(b+c) works
    but (b.b)is a scalar not a vector so cant be the same as
    (b.b)*b + (b.b)*c

    could someone please clarify
     
  4. Jul 30, 2009 #3
    3: (b.b)(b+a)
    is the same as
    5: (a.b).c

    scalar multiplied by a vector = vector
     
  5. Jul 30, 2009 #4
    lol what a stupid thread, wish I hadn't made it

    - suppose i could've done the same thing on paper
     
  6. Jul 30, 2009 #5

    Mark44

    Staff: Mentor

    I'm not sure what you concluded for 3 and 5.
    In your first post you have
    3) (b.b)b + a
    and then later you have (b.b)(b + a)
    b.b is a scalar
    (b.b)b is a scalar times a vector (= a vector)
    (b.b)b + a is a vector + a vector, which is a vector.

    (b.b)(b + a) is also a vector, but a different one from (b.b)b + a.

    5) (a.b).c is not a vector. This is a scalar dotted with a vector, which is not defined. The dot product is defined only for two vectors.
     
  7. Jul 30, 2009 #6
    5) (a.b).c is not a vector. This is a scalar dotted with a vector, which is not defined. The dot product is defined only for two vectors.[/QUOTE]

    But when you get the Scalar a.b, then multiply the vector c by the scalar don't you get a vector???

    e.g

    a=(2,2,2) b = (3,3,3) c = (4,4,4)

    (a.b).c
    a.b = 6 + 6 + 6 = 18

    then 18 * c
    18(4,4,4)
    =(18*4,18*4,18*4)
    =(72,72,72)
    isn't that the result when you multiply a scalar be a vector?
     
  8. Jul 31, 2009 #7

    Mark44

    Staff: Mentor

    But when you get the Scalar a.b, then multiply the vector c by the scalar don't you get a vector???
    [/quote]
    You are confusing scalar multiplication with the dot product. I am assuming that the periods you used in (a.b).c mean "dot product." In that case you have a scalar dotted with a vector, which is undefined.

    If, on the other hand, you had written (a.b)c (without the second period), then the multiplication would be scalar multiplication, which is defined for a scalar and a vector.
    No, it would be 18 . c, not 18 * c. This is where you are confusing the dot product with scalar multiplication.

    Dot product
    Inputs: two vectors
    Output: a scalar

    Scalar multiplication
    Inputs: a scalar and a vector
    Output: a vector

    Hope that's clear.
     
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