Question

I need help with 1.24

EXERCISE 1.20. Prove that every subspace VCR has an orthonora basis. HINT: Begin with an arbitrary basis. Do the following one besi member at a time: subtract from it ils projection onto the son of the premio basis members, and then scale it to make it of unit length. This is called the Grm-Schmidt process EXERCISE 1.21. Prove Lemma 1.16 EXERCISE 1.22. Is the converse of part (1) of Proposition 1.17 true? EXERCISE 1.23. Let y: 1 R3 be a regular space curve, and let PCR be a plane that does not intersect the image of y. If y comes closest to Pat time to prove that '(to) is parallel to P. EXERCISE 1.24. If lo e I is the time at which the curvey: R farthest from the origin, prove that y(to) is orthogonal to Y' (to). EXERCISE 1.25. If y: I R is a regular curve, prove that 10 = (0, 0) 3. Acceleration In this section, we interpret the second derivative of a regular curve as acceleration.

Answer 1

1.24) to EI MIR?. Considere 2 Correcto.rcto)) Idt _= 12C+214-to - d mat.net] It=to. d llrat 1121 dt t=to =0 - acreto) Victo)) = 0 - retol.misto) = 0 - mesto) is orthogonal to victo)

Него - to because d 11(A) 11 = 0 =/d India dt dt t=to since, IlmcAll does not change to e any value of it and mat). Lie. Irrt) L is constant.