- #1
JasonJo
- 429
- 2
1. calculate the length of the following paths:
f(t) = (7, t, t^2) over 1<t<3
the way i was taught in class to calculate the length of a curve is to integrate the magnitude of the velocity, but i can't seem to naturally integrate the magnitude of (0, 1, 2t)
similarly for:
f(t) = (cos(3t), sin(3t), 2t^(3/2)) 0<t<4
2. prove the bac-cab formula
aX(bXc) = b(a*c) - c(a*b)
where * is the dot product
what does b(a*c) mean?! how do i evaluate that?
i wrote aX(bXc) in terms of the component form, etc.
3. prove the length curve and curvature formulas.
5. prove aX(bXc) = (aXb)Xc + bX(aXc)
PLEASE HELP!
f(t) = (7, t, t^2) over 1<t<3
the way i was taught in class to calculate the length of a curve is to integrate the magnitude of the velocity, but i can't seem to naturally integrate the magnitude of (0, 1, 2t)
similarly for:
f(t) = (cos(3t), sin(3t), 2t^(3/2)) 0<t<4
2. prove the bac-cab formula
aX(bXc) = b(a*c) - c(a*b)
where * is the dot product
what does b(a*c) mean?! how do i evaluate that?
i wrote aX(bXc) in terms of the component form, etc.
3. prove the length curve and curvature formulas.
5. prove aX(bXc) = (aXb)Xc + bX(aXc)
PLEASE HELP!