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9 Let y: R→R" be a differentiable curve. Show that y(t) is constant if and only if y(t) and y'(t) are orthogonal for all t. 10

9 Let y: R→R" be a differentiable curve. Show that y(t) is constant if and only if y(t) and y'(t) are orthogonal for all t. 10

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 answer 1.9 only thanks
-9 Let y: R→R" be a differentiable curve. Show that y(t) is constant if and only if y(t) and y'(t) are orthogonal for all t. .10 Suppose that a particle moves around a circle in the plane ², of radius r centered at 0, with constant speed v. Deduce from the previous exercise that y(t) and y'(t) are both orthogonal to y'(t), so it follows that y"(t) = k(t)y(t). Substitute this result into the equation obtained by differentiating aft):16). to obtain k 21..2 Th
Transcribed Image Text:-9 Let y: R→R" be a differentiable curve. Show that y(t) is constant if and only if y(t) and y'(t) are orthogonal for all t. .10 Suppose that a particle moves around a circle in the plane ², of radius r centered at 0, with constant speed v. Deduce from the previous exercise that y(t) and y'(t) are both orthogonal to y'(t), so it follows that y"(t) = k(t)y(t). Substitute this result into the equation obtained by differentiating aft):16). to obtain k 21..2 Th
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