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

    3
    ReputationRep:
    Q:

    Points A, B and C have coordinates (5, -1, 0), (2, 4, 10) and (6, -1, 4) respectively.

    (a) Find the vectors \vec{CA} and \vec{CB}

    (b) Find the area of the triangle ABC

    (c) Point D is such that the point A, B, C and D form the vertices of a parallelogram. Find the coordinates of three possible positions of D.

    --------

    (a) \vec{CA} = \begin{pmatrix} -1 \\ 0 \\ -4 \end{pmatrix}

    \vec{CB} = \begin{pmatrix} -4 \\ 5 \\ 6 \end{pmatrix}

    (b) Area of triangle = 15.07 units^2

    (c) Need help in this part.

    Zacken any help with part (c) please?
    Offline

    22
    ReputationRep:
    What's the definition of parallelogram?
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by Zacken)
    What's the definition of parallelogram?
    A four sided shape, with opposite sides parallel I guess?
    Offline

    22
    ReputationRep:
    (Original post by SaadKaleem)
    A four sided shape, with opposite sides parallel I guess?
    Yep, so set up your D such that CD is parallel to AB or DA is parallel to another side or etc...
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by Zacken)
    Yep, so set up your D such that CD is parallel to AB or DA is parallel to another side or etc...
    Yes, I managed to sketch three possible shapes, however failed to deduce regardless, the coordinates of D.

    Probably missing out on something silly here.

    Vectors :argh:

    Offline

    22
    ReputationRep:
    (Original post by SaadKaleem)
    Yes, I managed to sketch three possible shapes, however failed to deduce regardless, the coordinates of D.

    Probably missing out on something silly here.

    Vectors :argh:
    Set D = (x, y, z)^{T} and then look at AD, CD, BD, or along those lines and equate AD with the opposite side of AD - since it's a parallelogram, then compare components, etc...
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by Zacken)
    Set D = (x, y, z)^{T} and then look at AD, CD, BD, or along those lines and equate AD with the opposite side of AD - since it's a parallelogram, then compare components, etc...
    Alright, got my answers.. This was my first shape-like vector question, so i struggled.

    Answers I got:

    \vec{OD 1} = \begin{pmatrix} 9 \\ -6 \\ -6 \end{pmatrix}

    \vec{OD 2} = \begin{pmatrix} 1 \\ 4 \\ 6 \end{pmatrix}

    \vec{OD 3} = \begin{pmatrix} 3 \\ 4 \\ 14 \end{pmatrix}

    So in coordinates (9, -6, -6), (1, 4, 6) and (3, 4, 14)

    Thank you Zacken
    Offline

    22
    ReputationRep:
    (Original post by SaadKaleem)
    Thank you Zacken
    First class work!
 
 
 
Poll
Do you agree with the PM's proposal to cut tuition fees for some courses?
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

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.