Explanation Given information : For two vectors A → and B → the Lagrange’s identity is given by ‖ A → × B → ‖ 2 = ( ‖ A → ‖ ⋅ ‖ B → ‖ ) 2 − ( A → ⋅ B → ) 2 , where ‖ A → ‖ denotes the magnitude of vector A → . Formula used : The formulae for scalar and vector products of two vectors and the trigonometric identity si n 2 θ + co s 2 θ=1 . Proof: Let θ be the angle between two given vectors v → and w → . The scalar product of vectors v → and w → is v → ⋅ w → = ‖ v → ‖ ‖ w → ‖ cosθ ⇒ ( v → ⋅ w → ) 2 = ( ‖ v → ‖ ‖ w → ‖ ) 2 co s 2 θ … (1) The vector product of vectors v → and w → is v → × w → = ‖ v → ‖ ‖ w → ‖ sinθ

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 9.4, Problem 52PS

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Toprove:The Lagrange’s identity.

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Calculus

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Toprove: The Lagrange’s identity.

Solution Summary: The author explains the formulae for scalar and vector products of two vectors and the trigonometric identity.

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