Turn on thread page Beta

2 questions watch

Announcements
    • Thread Starter
    Offline

    0
    ReputationRep:
    hi,
    i need help with 2 questions.

    1. find the equation of the plane that passes through

    u = (1,1,5)
    v = (-2,2,0)
    w = (3,-1,3)

    2.
    find the first three terms of the taylor series for sin x around x = pi

    thanks
    Offline

    2
    ReputationRep:
    1. You need a point, and two non-parallel vectors to get the equation of the plane.

    UV = v-u = -3i + j - 5k
    UW = w-u = 2i - 2j - 2k = a(i - j - k) , where 'a' is some constant.

    For the point, you can pick anything. Let's take (i + j + 5k), simply because it's the first one.

    Eq. plane: r = (i + j + 5k) + s(-3i + j - 5k) + t(i - j - k)
    Offline

    15
    ReputationRep:
    (Original post by manps)
    1. find the equation of the plane that passes through
    u = (1,1,5)
    v = (-2,2,0)
    w = (3,-1,3)
    One way is the solve the three simultaneous equations

    a + b + 5c = d
    -2a + 2b = d
    3a - b + 3c = d

    which will determine a,b,c,d up to scalar multiples

    The equation of the plane is then ax+by+cz=d

    Another is to find the cross product of v-u = (-3,1,-5) and w-u = (2,-2,-2) which will provide a normal vector - call it n=(n1,n2,n3)

    The equation of the plane is

    n1 x + n2 y + n3 z = n.u

    where "." is the scalar/dot product
    • Thread Starter
    Offline

    0
    ReputationRep:
    anyone got any ideas for part (b)
    Offline

    15
    ReputationRep:
    (Original post by manps)
    anyone got any ideas for part (b)
    taylor's theorem centred about pi says

    f(x) = f(pi) + f'(pi)(x-pi) + f''(pi)/2 (x-pi)^2 + f'''(pi)/6 (x-pi)^3 +...
 
 
 
Turn on thread page Beta
Updated: May 10, 2005

University open days

  • University of East Anglia
    All Departments Open 13:00-17:00. Find out more about our diverse range of subject areas and career progression in the Arts & Humanities, Social Sciences, Medicine & Health Sciences, and the Sciences. Postgraduate
    Wed, 30 Jan '19
  • Aston University
    Postgraduate Open Day Postgraduate
    Wed, 30 Jan '19
  • Solent University
    Careers in maritime Undergraduate
    Sat, 2 Feb '19
Poll
Brexit: Given the chance now, would you vote leave or remain?
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

Equations

Best calculators for A level Maths

Tips on which model to get

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

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.