Answered: Prove that if A and B are any vectors,…

Prove that if A and B are any vectors, then the vectors lBl A + lAl B and lBl A - lAl B are orthogonal such that A=(a1,a2,a3); B=(b1,b2,b3); IAI=(a12 ,a22 ,a32 ); IBI=(b12 ,b22 ,b32 ).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.4: The Dot Product

Problem 11E

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Question

Prove that if A and B are any vectors, then the vectors lBl A + lAl B and lBl A - lAl B are orthogonal such that A=(a₁,a₂,a₃); B=(b₁,b₂,b₃); IAI=(a₁² ,a₂² ,a₃² ); IBI=(b₁² ,b₂² ,b₃² ).

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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