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

    0
    ReputationRep:
    7) A curve has parametric equations

    x = e^2t, y =2t/(1 + t)

    (i) Find the gradient of the curve at the point where t = 0
    (ii) Find y in terms of x.

    9) The points A, B and C have coordinates (1, 3, ?2), (?1, 2, ?3) and (0, ?8, 1) respectively.
    (i) Find the vectors AB and AC.
    (ii) Show that the vector 2i ? j ? 3k is perpendicular to the plane ABC. Hence find the equation of
    the plane ABC.

    I tried to do nine by doing the dot product, but i couldnt get it to work?

    Anyone give me a clue please?
    Offline

    2
    ReputationRep:
    (Original post by fujitsum)
    7) A curve has parametric equations

    x = e^2t, y =2t/(1 + t)

    (i) Find the gradient of the curve at the point where t = 0
    (ii) Find y in terms of x.

    9) The points A, B and C have coordinates (1, 3, ?2), (?1, 2, ?3) and (0, ?8, 1) respectively.
    (i) Find the vectors AB and AC.
    (ii) Show that the vector 2i ? j ? 3k is perpendicular to the plane ABC. Hence find the equation of
    the plane ABC.

    I tried to do nine by doing the dot product, but i couldnt get it to work?

    Anyone give me a clue please?
    What about question 7, you stuck on both bits?
    • Thread Starter
    Offline

    0
    ReputationRep:
    Yep!
    • PS Reviewer
    Offline

    20
    ReputationRep:
    for question 7, show your working
    Offline

    2
    ReputationRep:
    (Original post by fujitsum)
    Yep!
    7)

    i) The gradient of a parametric curve would be dy/dt * dt/dx. (Can you find dt/dx?)

    ii) You need to find a way of writing this as a cartesian equation, so you'll need to get rid of the t.

    9) I assume the question marks are minus signs.
    • PS Reviewer
    Offline

    20
    ReputationRep:
    What are the ? meant to be?
    Offline

    2
    ReputationRep:
    (Original post by fujitsum)
    9) The points A, B and C have coordinates (1, 3, ?2), (?1, 2, ?3) and (0, ?8, 1) respectively.
    (i) Find the vectors AB and AC.
    (ii) Show that the vector 2i ? j ? 3k is perpendicular to the plane ABC. Hence find the equation of
    the plane ABC.

    I tried to do nine by doing the dot product, but i couldnt get it to work?

    Anyone give me a clue please?
    Assuming you're asking for a clue with part (ii), you're using a.b = |a||b|cos(x), right?

    If the plane and the vector are perpendicular, what's the angle between them? How does that affect the RHS?
    • Thread Starter
    Offline

    0
    ReputationRep:
    Yeah, the question marks are minus signs, don't know why its done that.

    I am really clueless?? I don't get how to differentiate anything on q7.
    Offline

    2
    ReputationRep:
    (Original post by fujitsum)
    Yeah, the question marks are minus signs, don't know why its done that.

    I am really clueless?? I don't get how to differentiate anything on q7.
     \frac{dy}{dx} = \frac{dy}{dt} * \frac{dt}{dx} = \frac{dy}{dt} * \frac{1}{\frac{dx}{dt}}

    You'll want to find the derivitive of y with respect to t, and the derivitive of t with respect to x. (This is the same as the reciprocal of the derivitive of x with respect to t).

    Do you know how to differentiate e^x and quotients?
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by EEngWillow)
    If the plane and the vector are perpendicular, what's the angle between them? How does that affect the RHS?
    I dooon't know?? :confused:
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by EEngWillow)
     \frac{dy}{dx} = \frac{dy/dt} * \frac{dt}{dx} = \frac{dy}{dt} * \frac{1}{\frac{dx}{dt}}

    You'll want to find the derivitive of y with respect to t, and the derivitive of t with respect to x. (This is the same as the reciprocal of the derivitive of x with respect to t).

    Do you know how to differentiate e^x and quotients?
    Nope, well, i might recognise it, but i don't have any of the assumed knowledge from core 3!
    Offline

    2
    ReputationRep:
    (Original post by fujitsum)
    Nope, well, i might recognise it, but i don't have any of the assumed knowledge from core 3!
    Just realised I ****ed up my LaTeX completely, equation is fixed now.

    When you differentiate e^5x, you'll get 5e^5x. You have e^2t, so you'll get?

    The quotient rule is dy/dx = (vdu - udv)/v^2, where u is the numerator and v the denominator. You use it when you have a fraction where both the numerator and denominator are functions of the variable you're differentiating with respect to.


    And for question 9: When two lines are perpendicular, the angle between them is 90 degrees. cos(90) = 0, so if they're perpendicular your scalar product will equal 0.
    • Thread Starter
    Offline

    0
    ReputationRep:
    2e^2t then!

    I'll revise quotient rule and have a crack at it then!

    How do you do the dot product correctly?

    I x'd the two vectors (A&B) together? That doesnt = 0 though?
 
 
 
  • 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
    What newspaper do you read/prefer?
    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.