Introduction to Electrodynamics 4e

Published by Pearson Education
ISBN 10: 9332550441
ISBN 13: 978-9-33255-044-5

Chapter 1 - Section 1.2 - Vector Algebra - Problem - Page 7: 3

Answer

Angle = 70.5 $^{\circ}$ or 109.5 $^{\circ}$. These two answers are supplementary (add up to 180 $^{\circ}$), so the answer depends on which one you decided to find.

Work Step by Step

Start with a cube with side lengths 1, and vertices ABCDEFGH as shown on the diagram. Construct vectors a,c, and d as defined in the diagram. Construct them in x,y,z components; and find their lengths which all equate to $\sqrt 3$. Two situations are discussed: the angle between vectors a and c, and the angle between vectors a and d. Using the dot product in component and abstract form, you work out the angles.
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