Results 1 to 2 of 2

Math Help - Intersection of line with YZ plane

  1. #1
    Newbie
    Joined
    May 2009
    Posts
    17

    Intersection of line with YZ plane

    Here I have a supposedly simple vector question but my answer seems to be wrong. What am I doing wrong?

    A(1,3,2) u= i + 3j +k v= 3j-k

    a) If vector AB = u - v what are coordinates of B

    AB = OB - OA

    OB = (u -v) + OA

    OB = (2,3,4)

    b)i) Write down the parametric equation of the line L, passing thorugh the point A in the direction of AB.

    L = OA + m(AB)

    L = (1,3,2) m(1,0,2)

    ii) What is the value of m at which L cross the YZ plane.

    L crosses the YZ plane when x= 0

    (0,y,z) = (1,3,2) + m(1,0,2)

    0 = 1 + m
    y = 3
    z= 2 + 2m

    My problem here is that the z turns out to be zero. This is not possible since it says it crosses the YZ plane. What is wrong with this?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by gva0324 View Post
    Here I have a supposedly simple vector question but my answer seems to be wrong. What am I doing wrong?

    A(1,3,2) u= i + 3j +k v= 3j-k

    a) If vector AB = u - v what are coordinates of B

    AB = OB - OA

    OB = (u -v) + OA

    OB = (2,3,4) ........... OK

    b)i) Write down the parametric equation of the line L, passing thorugh the point A in the direction of AB.

    L = OA + m(AB)

    L = (1,3,2) + m(1,0,2) ........... <<<<<<<<<

    ii) What is the value of m at which L cross the YZ plane.

    L crosses the YZ plane when x= 0

    (0,y,z) = (1,3,2) + m(1,0,2)

    0 = 1 + m
    y = 3
    z= 2 + 2m

    My problem here is that the z turns out to be zero. This is not possible since it says it crosses the YZ plane. What is wrong with this?
    All your considerations are OK.
    <br />
\left|\begin{array}{rcl}0& =& 1 + m\\ y &=& 3\\ z&=& 2 + 2m\end{array}\right.

    From the first equation you get m = -1. Then the point of intersection is P(0, 3, 0). The point of intersection is placed on the y-axis. But points of the y-axis belong to the yz-plane too.
    Attached Thumbnails Attached Thumbnails Intersection of line with YZ plane-schnttpkt_yzebene.png  
    Last edited by earboth; May 25th 2009 at 11:57 AM. Reason: adding a sketch
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Angle of intersection of the line and the plane
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: March 29th 2011, 10:58 AM
  2. Intersection point of a line and a plane
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 20th 2010, 03:28 PM
  3. Replies: 2
    Last Post: November 8th 2009, 08:33 AM
  4. Vectors: Intersection of a line and a plane
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 5th 2008, 08:59 PM
  5. Find the intersection of the line and plane
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 12th 2006, 08:03 PM

Search Tags


/mathhelpforum @mathhelpforum