find T,N,B curvature and torsion as a function of t for the space curve r(t)=sin t i+√2 cos t j+sin t k and find equation of normal and osculating planes
Find the curvature of the space curve. 1) r(t) - - 61+ (t + 10)j +(In(cost) + 6)k
5.3.15 Consider the quadratic form tx In (5.3.21) 1) Find a symmetric matrix A E R(n, n) such that q(x)-x' Ax for (ii) Compute the eigenvalues of A to determine whether q or A is pos- r E R" itive definite,
Find the curvature of the space curve. r(t) = -5 i + (10 + 2t)j + (t? + 8) k Ov-2021 2052 or OK 2(+1312
Find the curvature of the space curve. r(t) = -21 + (7 + 2t)j + (t2 + 5)k Ok=- 1 2012 Ver I 1 K= 2(2 + 1)3/2 Ok= 1 (2 + 1) 3/2 Oku- 1 2012-132
(b): Find the unit tangent vector T, the principal unit normal N, and the curvature k for the space curve, r(t) =< 3 sint, 3 cost, 4t >.
Tx N, for the vector-valued Find the vectors T and N, and the unit binomial vector B function r(t) and the given value of t. k, 3 to= 1 + Tx N, for the vector-valued Find the vectors T and N, and the unit binomial vector B function r(t) and the given value of t. k, 3 to= 1 +
1. a. Consider the curve defined by the following parametric equations: r(t) = et-e-t, y(t) = et + e-t where t can be any number. Determine where the particle describing the curve is when tIn(3) In(2). 0, ln(2) and In(3). Split up the work among your group Onex, vou l'ave found i lose live polnia, try to n"惱; wbai ille wlu le curve "u"ht lex k like. b. Verify that every point on the curve from the previous problem solves...
2. Let (a, b) nonvanishing. Denote the Frenet frame by {T, N, B} vector a E R3 with R3 be smooth with = 1 and curvature k and torsion r, both Assume there exists a unit Ta constant = COS a. circular helix is an example of such curve a) Show that b) Show that N -a 0. c) Show that k/T =constant ttan a 2. Let (a, b) nonvanishing. Denote the Frenet frame by {T, N, B} vector a...
Consider the following vector function. r(t) = 5t, ed, e) (a) Find the unit tangent and unit normal vectors T(t) and N(t). T(t) N(t) (b) Use this formula to find the curvature. k(t) =