## Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning

# Chapter 12 - Section 12.3 - The Dot Product - 12.3 Exercises - Page 813: 55

#### Answer

$cos ^{-1}(\frac{1}{ \sqrt 3} )\approx 55 ^ \circ$

#### Work Step by Step

Consider a cube with side length $1$ in which one diagonal goes from $(0,0,0)$ to $(1,1,1)$. An edge goes from $(0,0,0)$ to $(0,0,1)$ . $\theta = cos ^{-1}(\frac{\lt 1,1,1 \gt \cdot \lt 0,0,1 \gt}{\sqrt {1^2+1^2+1^2}\sqrt {0^2+0^2+0^2}})$ $\theta = cos ^{-1}(\frac{1}{ \sqrt 3} )\approx 55 ^ \circ$

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