Explanation Unit vectors form the basis of vector space, every vector in space is denoted as the linear combination of unit vectors. In a Cartesian coordinate system i , j , and k are the unit vectors corresponding to x , y , and z axis. The magnitude of each unit vector is 1. The cross product of two vectors A , and B is defined as below. A → × B → = A B sin θ (I) Here, θ is the angle between vector A , and B . The dot product of two vectors A , and B is defined as below. A → ⋅ B → = | A | | B | cos θ (II) The figure given below shows each unit vectors corresponding to x , y , and z axis, and its direction. The unit vectors are mutually perpendicular to each other Conclusion: Substitute, i ^ for A → , and B → , and 0 for θ in equation (I). i ^ × i ^ = 1 ⋅ 1 sin 0 ° = 0 Substitute, j ^ for A → , and B → , and 0 for θ in equation (I). j ^ × j ^ = 1 ⋅ 1 sin 0 ° = 0 Substitute, k ^ for A → , and B → , and 0 for θ in equation (I). k ^ × k ^ = 1 ⋅ 1 sin 0 ° = 0 Substitute, i ^ for A → , j ^ for B → , and 90 ° for θ in equation (I)

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN: 9781133104261

Author: Raymond A. Serway, John W. Jewett

Publisher: Cengage Learning

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Chapter 10, Problem 26P

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Prove equation 10.26 using the definition of vector product and concept of unit vectors.

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Principles of Physics: A Calculus-Based Text

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Prove equation 10.26 using the definition of vector product and concept of unit vectors.

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Prove equation 10.26 using the definition of vector product and concept of unit vectors.

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