r(t) = (x(t), y(t), z(t)) where æ(t) = – 2t + 3t + 3 y(t) = 2t – 2 2t2 + 5t z(t): Since all components are of no higher degree than quadratic, r'''(t) = < 0,0, 0 > and so the torsion of this curve is zero. This means the binormal vector B = B(t) is constant, and that the curve lies in a single plane. a) Find the equation of this plane. You may enter an equation like a(x – xo) + b(y – yo) + c(z – zo) = 0 or an equivalent expression.

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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This is a calculus 3 problem. Please explain each step clearly, no cursive writing. 

r(t) = (x(t), y(t), z(t)) where
x(t) = – 2t + 3t + 3
y(t) = 2t – 2
z(t)
2t? + 5t
Since all components are of no higher degree than quadratic, r'''
torsion of this curve is zero. This means the binormal vector B = B(t) is constant, and that the
curve lies in a single plane.
= < 0, 0, 0 > and so the
a) Find the equation of this plane.
You may enter an equation like a(x – xo) + b(y – yo) + c(z – zo)
expression.
= 0 or an equivalent
Transcribed Image Text:r(t) = (x(t), y(t), z(t)) where x(t) = – 2t + 3t + 3 y(t) = 2t – 2 z(t) 2t? + 5t Since all components are of no higher degree than quadratic, r''' torsion of this curve is zero. This means the binormal vector B = B(t) is constant, and that the curve lies in a single plane. = < 0, 0, 0 > and so the a) Find the equation of this plane. You may enter an equation like a(x – xo) + b(y – yo) + c(z – zo) expression. = 0 or an equivalent
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