Results 1 to 4 of 4

Math Help - I need help /w equations of some lines

  1. #1
    Newbie
    Joined
    Jul 2008
    Posts
    3

    I need help /w equations of some lines

    Hey everyone!

    I can't seem to solve these two questions. Any help is appreciated!

    1) A line has direction angles of 60 degrees, 45 degrees and 60 degrees. It passes through the point (1, -2, 5). Determine the vector equation of this line.

    2) Find the vector equation of a line that intersects the following 2 lines at 90 degrees.
    Line 1: (x,y,z) = (4, 8, -1) + a(2, 3, -4)
    Line 2: (x, y,z) = (7, 2, -1) + a(6, 1, 2)

    Thanks in advance
    -Mike
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by Mike49214 View Post
    ...

    2) Find the vector equation of a line that intersects the following 2 lines at 90 degrees.
    Line 1: (x,y,z) = (4, 8, -1) + a(2, 3, -4)
    Line 2: (x, y,z) = (7, 2, -1) + a(6, 1, 2)

    Thanks in advance
    -Mike
    1. The direction vectors of the lines are different therefore the lines are not parallel.
    2. An attempt to calculate the point of intersection doesn't yield a result therefore the lines are skewed.
    3. The cross-product of the direction vectors yield the direction perpendicular to both lines:

    (2,3,-4) \times (6,1,2) = (10, -28, -16)

    4. Now use this direction vector and any arbitrary point on L_1 to get the equation of a family of parallel lines:

    p: (x,y,z) = q \cdot (10,-28,-16)+\left((4, 8, -1) + r(2, 3, -4)\right) ....... r is considered to be constant with a certain line of the family.

    5. One (and only one) member of this family will intersect the line L_2:

    q \cdot (10,-28,-16)+\left((4, 8, -1) + r(2, 3, -4)\right) = (7, 2, -1) + s(6, 1, 2)

    6. Solve this system of linear equations for r, s and q.
    I've got q=-\frac{33}{190}~\wedge~s=-\frac{48}{95}~\wedge ~=-\frac{36}{95}

    7. The 2 points on different lines which have the smallest distance are:

    P\left(\frac{449}{95}~,~\frac{154}{95}~,~ -\frac{167}{95}\right) and Q\left(\frac{284}{95}~,~\frac{616}{95}~,~ \frac{97}{95}\right)

    8. Take one of the two points to calculate the equation of the line:

    p: (x,y,z) = \left(\frac{449}{95}~,~\frac{154}{95}~,~ -\frac{167}{95}\right) + t \cdot (10,-28,-16)

    My results do look really ugly, so better check my arithmetic. (If they are miraculously correct you are allowed to think two or three ugly words about the author of this question)
    Last edited by earboth; August 1st 2008 at 08:34 AM. Reason: additional calculations
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2008
    Posts
    3
    Quote Originally Posted by earboth View Post
    ...
    I've gone over it like 3 times and I can't see any errors in your calculations. Thanks a lot for the help, I appreciate it.

    I am still having trouble with the first question though, if anyone would be nice enough to lend a hand.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by Mike49214 View Post
    I've gone over it like 3 times and I can't see any errors in your calculations. Thanks a lot for the help, I appreciate it.

    I am still having trouble with the first question though, if anyone would be nice enough to lend a hand.
    Nobody of the forum has answered your question because it isn't understandable:

    You mention three angles. Which geometric objects form the angles? The line and axes? (if yes which axis belongs to which angle?), planes? (if yes which plane belongs to which angle?)

    ... and if you could provide a rough sketch that would really help us to help you.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Equations of Lines
    Posted in the Algebra Forum
    Replies: 2
    Last Post: October 3rd 2011, 10:09 PM
  2. equations of lines
    Posted in the Algebra Forum
    Replies: 24
    Last Post: September 16th 2011, 01:02 PM
  3. Help with equations of lines.
    Posted in the Algebra Forum
    Replies: 11
    Last Post: March 13th 2011, 06:09 PM
  4. Equations of lines
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: February 18th 2009, 01:01 PM
  5. equations of lines
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: February 21st 2007, 08:59 AM

Search Tags


/mathhelpforum @mathhelpforum