Since it is standard to use * as product and ^ as power, thisincreasesthe confusion!

a) Suppose that a.b = 0 [/quote]

And, now, having said you would use ^ for products, I have no idea what you could mean by a.b!

Assuming you mean 'a times b= 0" then either a= 0 or b= 0.

if "a times c" is NOT 0, then a cannot be 0 so b must be 0. But r^a apparently means "r times a" and if that is equal to 0, r must be equal to 0.[/quote]Find the solution r of the pair of equations:

r^a=b and r.c=n where a.c doesnt=0

Under what conditions does a solution exist if a.c=0? Find the most general solution in this case. Interpret your results geometrically. [/quote]

if a.c= 0 then either a= 0 or c= 0. If c= 0 and a is not, then the problem is just as before. If a= 0, we have r^0= 0 which is false for all r except 0 so we still must have r= 0. Of course, since you have made your notation as confusing as possible, I have no idea if this is what you mean!

This is a joke, right? There is NO q in your equation so we cannot say anything about it!b) Show that, if x doesnt=0 the equation r^d=xr+e has q unique and find it.

My attempt at a)

take vector product with a.Vectorproduct? This is the fist time you have said anything about vectors!

[tex]a^(r^a)=(a.a)r - (a.r)a=a^b

Hence r={1/|a|^2}a^b +ta where t = a.r / |a|*2

subsitute into r.c = n and we have

t =( n/a.c ) - [a,b,c]/(a.c)|a|*2

Therefore the solution is a single point.

I think that part is correct but I'm not sure, and have no idea how to continue with the problem! Please help!

Thank you![/QUOTE]