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1. 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.
2. 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.)
3. (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.
4. (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!
5. (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...
6. (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?
7. (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.
[..]
8. (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?
9. (Original post by Zacken)
[..]
(Original post by Pangol)
I misunderstood his response, hence why I'm asking for clarification.

Never mind, got it.
10. (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.
11. (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...
12. (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.
13. (Original post by an_atheist)
Legend. Thank you.
No problem.
14. (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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