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instead: (:) · ()- = ac – bd. a) Suppose that we also define a hyperbolic analogue of a rotation, using hyperbolic sine and cosine. A hyperbolic “rotation "is now given by (xcosh(0) + ysinh(0)\ ) = (sinh(0) + ycosh(0)) Rhyp(0)

instead: (:) · ()- = ac – bd. a) Suppose that we also define a hyperbolic analogue of a rotation, using hyperbolic sine and cosine. A hyperbolic “rotation "is now given by (xcosh(0) + ysinh(0)\ ) = (sinh(0) + ycosh(0)) Rhyp(0)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help. This problem involves verifying rotation properties through dot products. One picture shows the first part and the other shows the second part. Thank you.

Problem 15. Suppose that we change the definition of the dot product, defining a hyperbolic product *, where we introduce a negative sign and we have 3
Transcribed Image Text:Problem 15. Suppose that we change the definition of the dot product, defining a hyperbolic product *, where we introduce a negative sign and we have 3
instead: (6) - () = ac – bd. d. a) Suppose that we also define a hyperbolic analogue of a rotation, using hyperbolic sine and cosine. A hyperbolic “rotation "is now given by Rap(0) () - (xcosh(0) + ysinh(0) xsinh(0) + ycosh(0), Perhaps watching again the video on the dot product of January 13, show that this new version of the dot product is invariant under a hyperbolic rotation: Rhyp(0)u * Rhyp(0)v = u * v b) Determine and clearly draw the regions in the plane where vectors u = satisfy u * u = 0, and the regions where u * u > 0 and u * u < 0.
Transcribed Image Text:instead: (6) - () = ac – bd. d. a) Suppose that we also define a hyperbolic analogue of a rotation, using hyperbolic sine and cosine. A hyperbolic “rotation "is now given by Rap(0) () - (xcosh(0) + ysinh(0) xsinh(0) + ycosh(0), Perhaps watching again the video on the dot product of January 13, show that this new version of the dot product is invariant under a hyperbolic rotation: Rhyp(0)u * Rhyp(0)v = u * v b) Determine and clearly draw the regions in the plane where vectors u = satisfy u * u = 0, and the regions where u * u > 0 and u * u < 0.
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