Mathematics

Problem

Consider a triangular pyramid

ABCD

the position vector of whose angular points are

A(3, 0, 1)

B(-1, 4, 1)

C(5, 2, 3)

and

D(0, -5, 4)

. Let

G

be the point of intersection of the medians of the

\triangle BCD

. The length of the vector

AG

is a.

\sqrt{17}

\frac{\sqrt{51}}{3}

\frac{\sqrt{51}}{9}

\frac{\sqrt{59}}{4}