Results 1 to 2 of 2

Math Help - vectors urgent help

  1. #1
    Newbie
    Joined
    Jul 2007
    Posts
    11

    vectors urgent help

    the position vector of point A is 2i + 3j + k and the position vector of point B is 4i - 5j + 21k.

    a.) (i) show that vector AB = 2i - 8j + 20k
    (ii) find the unti vector u in the direction of vector AB
    (iii) show that u is perpendicular to vector OA.

    Let S be the midpoin=t of [AB]. THe line L1 passes through S and its parrallel to vector OA.
    b.) (i) find the position vector of S.
    (ii) Write down the equation of L1.

    The line L2 has equation r = (5i + 10j +10k) + s(-2i + 5j -3k).
    c.) explain why L1 and L2 are not parallel.
    d.) the lines L1 and L2 intersect at the point P. Find the position vector of P.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,212
    Thanks
    419
    Awards
    1
    Quote Originally Posted by miley_22 View Post
    the position vector of point A is 2i + 3j + k and the position vector of point B is 4i - 5j + 21k.

    a.) (i) show that vector AB = 2i - 8j + 20k
    (ii) find the unti vector u in the direction of vector AB
    (iii) show that u is perpendicular to vector OA.
    The vector \bold{AB} = \bold{B} - \bold{A} = (4i - 5j + 21k) - (2i + 3j + k) = 2i - 8j + 20k

    The unit vector is the vector in the same direction, but with unit length. So
    \hat{\bold{u}} = \frac{\bold{AB}}{|\bold{AB}|}

    To show that \hat{\bold{u}} is perpendicular to \bold{OA} = 2i + 3j + k, use the dot product. The dot product of two perpendicular vectors is 0.

    Quote Originally Posted by miley_22 View Post
    Let S be the midpoin=t of [AB]. THe line L1 passes through S and its parrallel to vector OA.
    b.) (i) find the position vector of S.
    (ii) Write down the equation of L1.
    Now this is just silly to me. Vectors can be moved all over the place without changing them, just as long as their length and direction aren't changed.

    I think what the problem is trying to say is "Place the tails of the vectors \bold{A} and \bold{B} at the origin. Then let S be the midpoint..." Only in this way is the wording unambiguous.

    So let's assume the rewritten problem is right. The heads of \bold{A} and \bold{B} are at (2, 3, 1) and (4, -5, 21), respectively. The midpoint S of these points is (3, -1, 11). So the vector \bold{OS} is
    \bold{OS} = 3i - j + 11k

    The vector form of a line in 3-D is
    \bold{r} = \bold{r_0} + \bold{A}t
    where \bold{r} is the position vector of a point on the line, \bold{r_0} is the position vector to a point that the line passes through, and \bold{A} is a vector, and t is a scalar parameter generating the points along the line. (The line will be parallel to \bold{A}.)

    So for L1 we want:
    \bold{r} = (3i - j + 11k) + (2i + 3j + k)t

    Quote Originally Posted by miley_22 View Post
    The line L2 has equation r = (5i + 10j +10k) + s(-2i + 5j -3k).
    c.) explain why L1 and L2 are not parallel.
    d.) the lines L1 and L2 intersect at the point P. Find the position vector of P.
    For c) consider this: What was the vector that forced L1 to be parallel to \bold{OA}? Similarly what is the vector that L2 is parallel to? Once you have these answers, the cross product of two parallel vectors is 0. Is this true for the L1 and L2 vectors?

    For d) you know that the (x, y, z) coordinate points of L1 are (3 + 2t, -1 + 3t, 11 + t). For L2 they are (5 - 2s, 10 + 5s, 10 - 3s). How can you find if they have a point in common? (ie. for what value of s and t are the two points the same?)

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Urgent: Vectors
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: September 12th 2012, 10:10 AM
  2. Urgent homework help!! Orthonormal vectors?
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: November 13th 2008, 10:40 AM
  3. Calculus Vectors URGENT HELP!
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: May 27th 2008, 06:21 PM
  4. Very Urgent: (distances of vectors)
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 7th 2008, 10:44 PM
  5. URGENT! vectors and planes.. need help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 30th 2008, 01:22 PM

Search Tags


/mathhelpforum @mathhelpforum