Mathematics

Problem

Let

\vec{a}

\vec{b}

\vec{c}

be three vectors such that

|\vec{a}|=1

|\vec{b}|=2

and

|\vec{c}|=3

. If the projection of

\vec{b}

along

\vec{a}

is equal to the projection of

\vec{c}

along

\vec{a}

and

\vec{b}

\vec{c}

are perpendicular to each other, find

|3\vec{a}-2\vec{b}+2\vec{c}|