Q1.3P Find the angle between the body ... [FREE SOLUTION]

91影视

Introduction to Electrodynamics

David J. Griffiths

Physics

4th edition Edition 路 613 pages

ISBN: 9780321856562

Chapter 1: Q1.3P (page 7)

Find the angle between the body diagonals of a cube.

Short Answer

Expert verified

The angle between the digonals is $70 . 52^{鈭�}$ .

Step by step solution

Explain the concept and draw the cube using given information

To find the angle between the diagonals, the vector diagonals must be evaluated and then the dot formula must be used.

The cube has 1 unit side and one of the corner is coinciding with the origin. using this information, the cube is drawn as follows:

Assume the vectors

The principle diagonals are $\overset{鈫�}{O M}$ and $\overset{鈫�}{B A}$ . The corrdinates of points O, M, A and B are $O = (0, 0, 0), M = (1, 1, 1), B = (0, 1, 0)$ and $A = (1, 0, 1)$ .

Find the vectors $\overset{鈫�}{O M}$ and $\overset{鈫�}{B A}$ .

$\overset{鈫�}{O M} = (1 - 0) i + (1 - 0) j + (1 - 0) k = i + j + k$

Solve the vector $\overset{鈫�}{B A}$ .

$\overset{鈫�}{B A} = (1 - 0) i + (0 - 1) j + (1 - 0) k = i - j + k$

Find the dot product between OM→ and AB→ .

The formula of the dot product of the vectors $\overset{鈫�}{O M}$ and $\overset{鈫�}{B A}$ is

$\overset{鈫�}{O M} \overset{鈫�}{B A} = |O M| |B A| \cos 胃, 胃$ is the angle between the vectos $\overset{鈫�}{O M}$ and $\overset{鈫�}{B A}$ .

Find the dot product of the vectors $\overset{鈫�}{O M}$ and $\overset{鈫�}{B A}$ .

$\overset{鈫�}{O M} . \overset{鈫�}{B A} = |O M| |B A| \cos 胃 2 = 3 \cos 胃 \cos 胃 = \frac{2}{3} 胃 = 70 . 52^{鈭�}$

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91影视

Find the angle between the body diagonals of a cube.

Short Answer

Step by step solution

Explain the concept and draw the cube using given information

Assume the vectors

Find the dot product between OM→ and AB→ .

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