Mathematics

Problem

If the magnitude of the vectors,

\vec{a}

\vec{b}

\vec{c}

are 3, 4, 5 respectively and

\vec{a}

and

\vec{b} + \vec{c}

\vec{b}

and

(\vec{c} + \vec{a})

\vec{c}

and

(\vec{a} + \vec{b})

are mutually perpendicular, then find the magnitude of

(\vec{a} + \vec{b} + \vec{c})