Question

if a,b,c are three mutually perpendicular vectors of equal magnitude, find the angle between θ and a+b+c

Answer 1

It is given that, \(|\vec a|=|\vec b|=|\vec c|= \lambda\) (say) and \(\vec a,\vec b, \vec c\) are mutually perpendicular vectors.

Therefore, \(|\vec a+\vec b+\vec c|=\sqrt 3\lambda\)

Let θ be the angle which \(\vec a+\vec b+ \vec c\) makes with \(\vec a.\)

Then,