Hi, im really stuck on this question so would be very grateful if someone could help me with it!
Thanks
Gemma
To get rid of the absolute values square both sides of the given equation:
$\displaystyle |\vec a + \vec b| = |\vec a - \vec b|~\implies~(\vec a + \vec b)^2 = (\vec a - \vec b)^2$
$\displaystyle (\vec a)^2+2\cdot \vec a \cdot \vec b +(\vec b)^2=(\vec a)^2-2\cdot \vec a \cdot \vec b +(\vec b)^2~\implies~2\cdot \vec a \cdot \vec b = -2\cdot \vec a \cdot \vec b~\implies~4\cdot \vec a \cdot \vec b = 0$
I'll leave the rest for you.