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    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.
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    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.)
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    (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.
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    (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!
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    (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...
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    (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?
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    (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.
    [..]
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    (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...
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    (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.
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    (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.
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    (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...
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    (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.
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    (Original post by an_atheist)
    Legend. Thank you.
    No problem.
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    (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.
 
 
 
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