Mathematics

Problem

Vectors

\mathbf{u}

and

\mathbf{v}

have magnitudes

8

and

6

respectively, and the angle between them is

45^\circ

. Let

\mathbf{w}=2\mathbf{u}-\mathbf{v}

. The value of

\mathbf{u}\cdot\mathbf{w}

is a)

128 + 24\sqrt2

64 - 24\sqrt2

128 - 24\sqrt2

104