9 r(+) =( 3t² 37,363) (56", 3 cosb.6+ 324) V2 Lt) = (3,3,3) find the cosive...
(1 point)
Given
R(t)=e4tcos(3t)i+e4tsin(3t)j+3e4tkR(t)=e4tcos(3t)i+e4tsin(3t)j+3e4tk
Find the derivative R′(t)R′(t) and norm of the derivative.
R′(t)=R′(t)= ∥R′(t)∥=‖R′(t)‖=
Then find the unit tangent vector T(t)T(t) and the principal
unit normal vector N(t)N(t)
T(t)=T(t)= N(t)=N(t)=
(1 point) Given R(t) = cos(36) i + e sin(3t) 3 + 3e"k Find the derivative R') and norm of the derivative. R'(t) = R' (t) Then find the unit tangent vector T(t) and the principal unit normal vector N() T(0) N() Note: Yn can can on the hom
2 A particle's position as a function is given by R (3t-4nty +(2P)-2 (a) Find the particle's velocity function v(t). (b) Find the particle's acceleration a(t). (c) Is there a time when a, and ay are equal? If yes, when? (d) Given S-(t+2nt)+-3r)j+22, find R.S (e) Find R x Š and label itT Find the angle between R and S. (g) What is the angle between S and 7?
for the curve r(t) find an equation for the indicated
plane at the given value of t
56) r(t) (t2-6)i+ (2t-3)j+9k; osculating plane at t=6 A) x+ y+(z+9)=0 C)x+y+ (z-9)-0 56) B) z-9 D) z -9 (3t sint+3 cos t)i + (3t cos t-3 sin t)j+ 4k; normal plane at t 1.5r.. A) y=-3 57) r(t) 57) B) y 3 C)x-y+z-3 D) x+y+z=-3
56) r(t) (t2-6)i+ (2t-3)j+9k; osculating plane at t=6 A) x+ y+(z+9)=0 C)x+y+ (z-9)-0 56) B) z-9 D)...
45 Find L 32 +25-3 5 -3t (write 5/6 by 6' , e^{-3t} by e and sin(2t) or cos(3t) by sin(2t) or cos(3t)). **{3+2-3)
1. (1 point) Find two vectors vi and v2 whose sum is (-3,0), where Vi is parallel to(-2,-4) while v2 is perpendicular to-2,-4) and Answer(s) submitted: (incorrect) 2. (1 point) Find the angle θ between the vectors a- 10i -j- 5k and b 2i+j- 21k Answer (in radians): θ Answer(s) submitted: (incorrect) 3. (1 point) Find a vector a that has the same direction as -6,5,6) but has length 3. Answer: a Answer(s) submitted: (incorrect) 4. (1 point) Suppose we...
[3] Given: u = -81 +6j vi- j = -101 Point Pat (-17, -v2), point 9 at (-9, 11), and point Rat (8.-15) Five of the following six parts are each worth 3 points. Part b is worth 5 points. a) Find the position vector, in x + yj form, for the vector whose initial point is R and whose terminal point is g. b) Sketch the position vector determined by point P, and then find its magnitude and direction....
QUESTION 6 -1 Find L 45 S2 + 25-3 5 (write 5/6 by 7' -3t e^{-3t} by e and sin(2t) or cos(3t) by sin(2t) or cos(3t)).
plz
show all steps in a readable handwritting for problem number 5,6
& 7
5) Find T(t),n(t), B(t),r(t),k(t) and ρ(t) for r(t)=tT+(3t-1) 6) Find the graph of the osculating circle to the curve y = x2 at the point (1,1) 7) Let r(t) = t21-7j+ 2t2k.Given thata= a:T+aM a) Find the tangential component of the acceleration. b) Find the normal component of the acceleration directly (via the formula for an) and indirectly (using |ã | and ar). Show that they...
only 6 please!!
4. R 5 3 e 12 Find sin (9). COS C), tan 6. Find the measure of each angle in the triangle shown in the figure below. 12 A 10 7 B
Find the point, P, at which the line intersects the plane. x= -6 - 3t, y = -3- 9t, z= -6+ 4t: 8x + 2y +6z = 5 The point, P, at which the line intersects the plane is (00). (Simplify your answer. Type an ordered triple.)