Chapter 12 - Vectors and the Geometry of Space - 12.3 The Dot Product - 12.3 Exercises - Page 852: 10

$-2000{\sqrt 2}$

$|a|=80,|b|=50$ , $ \theta =\frac{3\pi}{4}$ Dot product formula: $a \cdot b=|a||b|cos \theta$ $a \cdot b=(80)(50)cos \frac{3\pi}{4}$ $a \cdot b=4000(-\frac{1}{\sqrt 2})$ $a \cdot b=4000(-\frac{\sqrt 2}{ 2})$ $a \cdot b=-2000{\sqrt 2}$