Results 1 to 5 of 5
Like Tree3Thanks
  • 1 Post By Prove It
  • 1 Post By sakonpure6
  • 1 Post By romsek

Math Help - Vectors #2

  1. #1
    Member
    Joined
    Jan 2013
    From
    Australia
    Posts
    166
    Thanks
    3

    Vectors #2

    The paths of two aeroplanes in an aerial display are simultaneously defined by the vectors:
    r1(t) = (16 - 3t)i + tj + (3 + 2t)k
    r2(t) = (3 + 2t)i + (1 + t)j + (11 - t)k

    t represents time in minutes. Find:
    a) the position vector of the first plane after one minute.
    r1(1) = 13i + j + 5k

    b) the unit vectors parallel to the flights of each of the two planes
    The inclusion of t has thrown me off.

    c) the acute angle between their lines of flight, correct to two decimal places

    d) the point at which their two paths cross
    I can do this for vectors in two dimensions, but not three.

    e) the vector which represents the displacement between the two planes after t seconds


    If you could walk me through this question, that would be great. Bear in mind that most of this is new to me.

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,548
    Thanks
    1418

    Re: Vectors #2

    I don't see why the inclusion of "t" should throw you off. For any vector $\displaystyle \begin{align*} \mathbf{a} \end{align*}$, its unit vector parallel to $\displaystyle \begin{align*} \mathbf{a} \end{align*}$ is $\displaystyle \begin{align*} \hat{\mathbf{a}} = \frac{\mathbf{a}}{ \left| \mathbf{a} \right| } \end{align*}$. It doesn't matter if this vector happens to be a function of another variable...
    Thanks from Fratricide
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member sakonpure6's Avatar
    Joined
    Sep 2012
    From
    Canada
    Posts
    413
    Thanks
    32

    Re: Vectors #2

    For c) use the following equation: cos \theta = \frac{Vector 1 (dot) Vector2}{|Vector 1| \times |Vector 2|}

    For d) to find the intersection of two vectors in 3D, first you must come up with the parametric equation of each vector, then substitute the x and y (or z) value of Vector 1 into that of Vector 2 respectively and that will yield two new equations of which each contains 2 unknown parameter values. Solve for one of the variables, and plug in the corresponding value back to the original Parametric, thus yielding the (x,y,z) coordinates of the intersection.
    Last edited by sakonpure6; April 18th 2014 at 12:35 PM.
    Thanks from Fratricide
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Jan 2013
    From
    Australia
    Posts
    166
    Thanks
    3

    Re: Vectors #2

    Quote Originally Posted by Prove It View Post
    I don't see why the inclusion of "t" should throw you off. For any vector $\displaystyle \begin{align*} \mathbf{a} \end{align*}$, its unit vector parallel to $\displaystyle \begin{align*} \mathbf{a} \end{align*}$ is $\displaystyle \begin{align*} \hat{\mathbf{a}} = \frac{\mathbf{a}}{ \left| \mathbf{a} \right| } \end{align*}$. It doesn't matter if this vector happens to be a function of another variable...
    That's what I thought, but when I plug in the values I get a horrible fraction containing many "t"s that shouldn't be there.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,454
    Thanks
    944

    Re: Vectors #2

    Quote Originally Posted by Fratricide View Post
    That's what I thought, but when I plug in the values I get a horrible fraction containing many "t"s that shouldn't be there.
    The vectors parallel to the line of flight won't have a $t$ in them in this situation of linear motion. rewrite your $r_1, r_2$ as

    $r_k(t)=\vec{r}_k(0) + \vec{v_k}t$

    The vector $v_k$ is the vector that is parallel to your line of motion. (It's the velocity vector)
    Thanks from Fratricide
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: November 15th 2011, 05:10 PM
  2. Replies: 3
    Last Post: June 30th 2011, 08:05 PM
  3. Replies: 2
    Last Post: June 18th 2011, 10:31 AM
  4. [SOLVED] Vectors: Finding coefficients to scalars with given vectors.
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: January 23rd 2011, 12:47 AM
  5. Replies: 4
    Last Post: May 10th 2009, 06:03 PM

Search Tags


/mathhelpforum @mathhelpforum