Vector problems?

Question

(a)show that a * (b * a) is zero for all vectors a and b. (b) What is the magnitude of a * (b * a) if there is an angle between the directions of a and b?

Answer 1

a * (b * a) can be equal 0 for all vectors only if you mean the mixed product of this vectors, i.e.:
a * [b * a], where the breckets [] mean the vector product. In this case it can be solved.
For any vectors a, b, c its truth (property of the mixed product):
a*[b*c]=b*[c*a]=c*[a*b];
your c=a, thus using the first equation you receive:
a*[b*a]=b*[a*a], but the vector product of two equal vectors
[a*a]=0. So you have:
a*[b*a]=b*[a*a]=0, for any a and b.
The magnitude of this vector is 0, because its a null-vector.

Answer 2

Part (a) of this question makes no sense.

(a) a*(b*a) is NOT zero for any vectors a and b. In fact, it is only zero if a and b point in the same direction, such that the angle between them is zero.

(b) First, let c = b * a
So magnitude of c is |a||b|Sin(anglebetweenaandb)
Then we must remember that the cross product will give us a vector perpendicular to BOTH a and b, so
|a*(b*a)| = |a|*|a||b|Sin(anglebetweenaandb)*sin(90)