Question

What is the magnitude of A X ( B X A ) if there is an angle φ = 50.0° between the directions a of and b ? Assume a = 9.8 and b = 8.1.

> from an example of this problem solved previously I got 595.9
through B X A=ab*sin φ
9.8*8.1*sin(50)=60.8

then A X B = ab*sin φ
9.8*60.8*sin(90)= 595.9

I have a few problems with understanding this answer.
for one, it feels far to large of a number to be correct. but I don't understand the problem to begin with so that's hard to judge.
Secondly, because B X A= -( A X B ) shouldn't the answer have a negative sign? Or is it because the question specifically asks for the magnitude that the negative sign is left off?

Answer 1

Given that, 

the magnitude of two vectors, a = 9.8 and b =  8.1

θ = angle between the two vectors = 50^ο 

Here, a x (b x a) = a x (absinθ)

                           = a²bsinθ

                           = (9.8)² x 8.1 x sin(50)

                           = 595.92 [Ans.]