Mathematics

Problem

Let

a, b, c

, be vectors of length 3, 4, 5 respectively and

a

be perpendicular to

(b + c)

b

(c + a)

and

c

(a + b)

, then the value of

(a + b + c)

is a.

2\sqrt{5}

2\sqrt{2}

10\sqrt{5}

5\sqrt{2}