Problem 4: It should be obvious that the magnitude of a vector is independent of the choice of coordinate system. This implies that r·r is the same for any set of axes. Use this to prove that the dot product of two different vectors r.s is also independent of coordinate system. [Hint: Consider the length of r + s.]
Problem 4: It should be obvious that the magnitude of a vector is independent of the choice of coordinate system. This implies that r·r is the same for any set of axes. Use this to prove that the dot product of two different vectors r.s is also independent of coordinate system. [Hint: Consider the length of r + s.]
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![Problem 4: It should be obvious that the magnitude of a vector is independent of the
choice of coordinate system. This implies that r r is the same for any set of axes. Use this
to prove that the dot product of two different vectors r.s is also independent of coordinate
system. [Hint: Consider the length of r + s.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29c74d06-0f3b-4eb2-9c9d-dbbc1918002c%2F3b006559-cce9-4d0a-8e70-43f5414b56b3%2Fv9hn3s_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 4: It should be obvious that the magnitude of a vector is independent of the
choice of coordinate system. This implies that r r is the same for any set of axes. Use this
to prove that the dot product of two different vectors r.s is also independent of coordinate
system. [Hint: Consider the length of r + s.]
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