Turn on thread page Beta
    • Community Assistant
    • Thread Starter
    Offline

    15
    ReputationRep:
    Community Assistant
    Need some help with a vectors question

    A vector x satisfies the equation x + (x.a)*b = c where a,b,c are constant vectors such that a.b =/= -1
    Assuming b and c are not parallel, using the form x = sb + tc + u(bxc) determine possible values of s,t,u and hence find x

    I've tried a direct substitution of the expression into the equation, which has left me with sb + tc + u(bxc) + (s*b.a + t*c.a + u*(bxc).a)*b = c. I'm not entirely sure I've expanded the dot porduct in the bracket correctly and I'm not sure where to go from here.
    Offline

    12
    ReputationRep:
    When you say

    (Original post by an_atheist)
    A vector x satisfies the equation x + (x.a)*b = c
    is the * supposed to be a vector product? If so, this doesn't make sense, because x.a is a scalar, and so cannot be vector producted with b. So that's probably not what it means, and I need to be further educated! (It probably doesn't mean this because you have used x to represent vector product elsewhere.)
    • Community Assistant
    • Thread Starter
    Offline

    15
    ReputationRep:
    Community Assistant
    (Original post by Pangol)
    When you say



    is the * supposed to be a vector product? If so, this doesn't make sense, because x.a is a scalar, and so cannot be vector producted with b. So that's probably not what it means, and I need to be further educated! (It probably doesn't mean this because you have used x to represent vector product elsewhere.)
    I used * to mean times. It got confusing using x to descibe the vector product and times.
    Offline

    12
    ReputationRep:
    (Original post by an_atheist)
    I used * to mean times. It got confusing using x to descibe the vector product and times.
    Oh I see - it is just the scalar x.a multiplied by the vector b.

    Edited to add: In which case, I'm afraid I don't have any ideas!
    Offline

    22
    ReputationRep:
    (Original post by an_atheist)
    Need some help with a vectors question

    A vector x satisfies the equation x + (x.a)*b = c where a,b,c are constant vectors such that a.b =/= -1
    Assuming b and c are not parallel, using the form x = sb + tc + u(bxc) determine possible values of s,t,u and hence find x

    I've tried a direct substitution of the expression into the equation, which has left me with sb + tc + u(bxc) + (s*b.a + t*c.a + u*(bxc).a)*b = c. I'm not entirely sure I've expanded the dot porduct in the bracket correctly and I'm not sure where to go from here.
    The question gives you a very big hint by mentioning a.b.

    So dot both sides by a to get x.a + (x.a)(a.b) = c.a, then x.a = c.a / (1+a.b), can you see why a.b is restricted to not be -1 now?

    Now that you know x.a, you can sub that into your original equation and solve for x.

    Edit: this doesn't quite do it in the way your question wanted it done, but this is a lot faster than assuming x has that form and blah...
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (Original post by an_atheist)
    Need some help with a vectors question

    A vector x satisfies the equation x + (x.a)*b = c where a,b,c are constant vectors such that a.b =/= -1
    Assuming b and c are not parallel, using the form x = sb + tc + u(bxc) determine possible values of s,t,u and hence find x

    I've tried a direct substitution of the expression into the equation, which has left me with sb + tc + u(bxc) + (s*b.a + t*c.a + u*(bxc).a)*b = c. I'm not entirely sure I've expanded the dot porduct in the bracket correctly and I'm not sure where to go from here.
    You sure you got that question correctly...?

    x.a is a scalar product which cannot be crossed with a vector b. I assume * means the cross product?
    Offline

    22
    ReputationRep:
    (Original post by RDKGames)
    You sure you got that question correctly...?

    x.a is a scalar product which cannot be crossed with a vector b. I assume * means the cross product?
    (Original post by Pangol)
    When you say [...] is the * supposed to be a vector product?
    (Original post by an_atheist)
    I used * to mean times. It got confusing using x to descibe the vector product and times.
    [..]
    Offline

    12
    ReputationRep:
    (Original post by RDKGames)
    You sure you got that question correctly...?

    x.a is a scalar product which cannot be crossed with a vector b. I assume * means the cross product?
    We've already resolved this with our discussion upthread...
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (Original post by Zacken)
    [..]
    (Original post by Pangol)
    We've already resolved this with our discussion upthread...
    I misunderstood his response, hence why I'm asking for clarification.

    Never mind, got it.
    Offline

    22
    ReputationRep:
    (Original post by RDKGames)
    I misunderstood his response, hence why I'm asking for clarification.
    It means normal scalar multiplication, like 1*2...

    It also clearly does not mean the dot product; you cannot take the dot product of a number and a vector.
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (Original post by Zacken)
    It means normal scalar multiplication, like 1*2...

    It also clearly does not mean the dot product; you cannot take the dot product of a number and a vector.
    Yeah, I got it...
    • Community Assistant
    • Thread Starter
    Offline

    15
    ReputationRep:
    Community Assistant
    (Original post by Zacken)
    The question gives you a very big hint by mentioning a.b.

    So dot both sides by a to get x.a + (x.a)(a.b) = c.a, then x.a = c.a / (1+a.b), can you see why a.b is restricted to not be -1 now?

    Now that you know x.a, you can sub that into your original equation and solve for x.

    Edit: this doesn't quite do it in the way your question wanted it done, but this is a lot faster than assuming x has that form and blah...
    Legend. Thank you.
    Offline

    22
    ReputationRep:
    (Original post by an_atheist)
    Legend. Thank you.
    No problem.
    Offline

    11
    ReputationRep:
    (Original post by an_atheist)
    Need some help with a vectors question

    A vector x satisfies the equation x + (x.a)*b = c where a,b,c are constant vectors such that a.b =/= -1
    Assuming b and c are not parallel, using the form x = sb + tc + u(bxc) determine possible values of s,t,u and hence find x

    I've tried a direct substitution of the expression into the equation, which has left me with sb + tc + u(bxc) + (s*b.a + t*c.a + u*(bxc).a)*b = c. I'm not entirely sure I've expanded the dot porduct in the bracket correctly and I'm not sure where to go from here.
    I won't comment on the answer, but I will say that this question would be much more comprehensible with a bit of latex.
 
 
 
Poll
Favourite type of bread
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.