Vector Algebra: Proving Mutually Perpendicular Vectors

[physixguru]

Homework Statement

a(v), b(v) and c(v) are three vectors. if a(v) x b(v) = c(v) and b(v) x c(v)= a(v)
Show that b(mod)= 1 and a(mod)=c(mod) and the three vectors are mutually perpendicular.
(v) denotes vector and (mod) denotes magnitude.
2. Homework Equations [/]

NA.

The Attempt at a Solution

Got some of it.Need a bit more explanation.

 

[Defennder]

To show that they are perpendicular, you need to show that $$\vec{a} \cdot \vec{b} = 0$$, since you already know that vector c is perpendicular to both a and b. See if you can apply this to what you are given.

As for the other two, one follows from the other. Just use the formula for magnitude of vector product on both given vector equations and compare them.

This should help:
http://en.wikipedia.org/wiki/List_of_vector_identities

 

[physixguru]

Thanks bro.How did you know if c was perpendicular to both?

 

[elbarto]

because C is the cross product of A and B, hence it must be perpendicular to both vectors.

 

[physixguru]

Thanks lord.I missed such a silly thing.