Results 1 to 6 of 6

Thread: Vector addition cases

  1. #1
    Senior Member
    Joined
    Mar 2017
    From
    Massachusetts
    Posts
    329
    Thanks
    2

    Question Vector addition cases

    I would like to know whether I am correct in my thinking below.

    You can add two vectors using basic arithmetic only when either two cases occur:

    (1) the vectors are parallel to each other
    (2) the vectors direction are opposite of each other (in which case, you could multiply one of the vectors by -1 in order to make them be parallel to each other, and then (1) would apply).

    Otherwise, you would have to use those fancy triangle laws and follow tip-to-tail methods etc.

    Is this correct? Please help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2010
    Posts
    3,728
    Thanks
    1521

    Re: Vector addition cases

    I am not sure what you mean.

    $$\begin{bmatrix}x_1 \\ x_2 \\ \vdots \\ x_n\end{bmatrix} + \begin{bmatrix}y_1 \\ y_2 \\ \vdots \\ y_n\end{bmatrix} = \begin{bmatrix}x_1+y_1 \\ x_2+y_2 \\ \vdots \\ x_n+y_n\end{bmatrix}$$

    This has the effect of the tip-to-tail method. The resultant vector will be the third side of the triangle.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    22,154
    Thanks
    3046
    Awards
    1

    Re: Vector addition cases

    Quote Originally Posted by otownsend View Post
    I would like to know whether I am correct in my thinking below.
    You can add two vectors using basic arithmetic only when either two cases occur:
    (1) the vectors are parallel to each other
    (2) the vectors direction are opposite of each other (in which case, you could multiply one of the vectors by -1 in order to make them be parallel to each other, and then (1) would apply).
    I too am not sure what you mean. You seem to have a somewhat odd idea of vectors.
    A vector is a hybrid for mathematics in that vectors have length & direction. Therefore, vectors are equivalent classes. Were use vector spaces to as models. You posted this in a calculus forum. So it is usual that we use $\mathbb{R}^n,~n=2,3,4$ as the setting for your problems.

    Therefore, in a given space, say $\mathbb{R}^3$, we can add any two vectors. There are no restrictions as long as we are in the same space. (i.e. vectors from $\mathbb{R}^3$ cannot be added to vectors in $\mathbb{R}^n$ if $n\ne 3)$. Two vectors are parallel in the same direction if they are positive multiples of each other, if negative multiples then parallel in opposite directions.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Oct 2009
    From
    Brisbane
    Posts
    1,077
    Thanks
    321

    Re: Vector addition cases

    Perhaps you are meaning that you can add vector a with vector ka which is parallel to it to get a+ka = (1+k)a

    but you can't algebraically simplify a+b if a and b are not parallel (ie not scalar multiples).

    (using bold to represent vectors)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Mar 2017
    From
    Massachusetts
    Posts
    329
    Thanks
    2

    Re: Vector addition cases

    Debsta's response was exactly what I was looking for. Thank you for your clarification!
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    22,154
    Thanks
    3046
    Awards
    1

    Re: Vector addition cases

    Quote Originally Posted by otownsend View Post
    You can add two vectors using basic arithmetic only when either two cases occur:
    (1) the vectors are parallel to each other
    (2) the vectors direction are opposite of each other (in which case, you could multiply one of the vectors by -1 in order to make them be parallel to each other, and then (1) would apply).
    Quote Originally Posted by Debsta View Post
    Perhaps you are meaning that you can add vector a with vector ka which is parallel to it to get a+ka = (1+k)a
    but you can't algebraically simplify a+b if a and b are not parallel (ie not scalar multiples).
    (using bold to represent vectors)
    Quote Originally Posted by otownsend View Post
    Debsta's response was exactly what I was looking for.
    It may have been what you were looking for, but it is not what you asked.
    We can add any two vectors in the same space using simple number operations.
    You seem to need to go to a good textbook on vector-calculus. Look into scalar multiplication.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Vector Addition
    Posted in the Math Topics Forum
    Replies: 6
    Last Post: Sep 8th 2015, 02:28 PM
  2. Vector Addition - 2
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: Sep 4th 2015, 02:20 PM
  3. Dedekind Cut Addition Degenerate Cases
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: Sep 8th 2010, 08:17 AM
  4. help with applications of vector addition
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: Jul 7th 2010, 07:31 PM
  5. Vector addition
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: Dec 8th 2008, 06:51 AM

Search Tags


/mathhelpforum @mathhelpforum