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

    0
    ReputationRep:
    The vector equation of the line L in the plane passing through the points A and B with
    position vectors a = (1,2) and b = (4,3) respectively is
    r = a + t(b-a) = (1,2) + t(3,1)
    (i.e. the set of vectors which are a plus some real multiple of the vector from a to b.)
    (a) Use the dot product to find the point P on the line which is closest to the origin
    (0,0).
    (b) Give the vector equation of the line through the origin which is orthogonal to the
    given line.

    Anycnt know how to solve this question or can offer any advice?
    Offline

    14
    You want the dot-product of the gradient of r with the gradient of a vector running through (0,0) to be zero. This is because the closest point to (0,0) on r will be where the perpendicular vector of r, running through (0,0), intersects r. So < (3,1) , (x,y) > say. Solve for x,y, and this gives you the gradient of your perpendicular vector. So the perpendicular vector will be of the form n = s(x,y) for some parameter s, and your found values of x and y. Now solve r=n for t, insert that value of t back into the eqn for r to find the point, and you're done.
 
 
 
  • 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
    Have you ever participated in a Secret Santa?
    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

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