Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    2
    ReputationRep:
    The question is a line called L1, passes through the point A (2,0,2) and has the equation

    R = (2,0,2) + T (2,6,-3)

    The line L2 is parralel to this line and passes through the points B (4,4,-5) and C (0, -8, 1). P is the point on the line L1 such that angle CPA is a right angle, find the value of the parameter T at p.

    i need to draw a sketch but am unsure how, im perplexted at this question any ideas? have I not made it clear enough?
    • Study Helper
    Offline

    13
    Study Helper
    (Original post by SunDun111)
    The question is a line called L1, passes through the point A (2,0,2) and has the equation

    R = (2,0,2) + T (2,6,-3)

    The line L2 is parralel to this line and passes through the points B (4,4,-5) and C (0, -8, 1). P is the point on the line L1 such that angle CPA is a right angle, find the value of the parameter T at p.

    i need to draw a sketch but am unsure how, im perplexted at this question any ideas? have I not made it clear enough?
    Sketch doesn't have to be accurate.

    Key point is you have two parallel lines. Mark B,C on one, and A on the other.
    Offline

    0
    ReputationRep:
    A diagram is helpful for the question simply to make it clearer to you what you need to do, but doesn't need to be accurate as already mentioned (and is by no means necessary once you are comfortable with this type of question).

    Here's how to solve the question:
    Since APC makes a right angle, you know that the scalar product of the vectors AP and CP is zero. You can find these vectors in terms of t and then simply multiply out the corresponding components (using the scalar product) to get a quadratic in t which can be easily solved (you know the quadratic equals 0 as I mentioned before).
    Spoiler:
    Show
    t = -1, you'll also get t = 0 from the quadratic but this simply tells you that the zero vector dotted with vector CP is zero, which is true but not helpful.

    By the way, to solve the next part of the question you simply need to find the magnitude of CP using your calculated value for t, as this perpendicular line between the two lines is the shortest distance.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Has a teacher ever helped you cheat?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Write a reply...
    Reply
    Hide
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.