The vector function r(t) = (1+2 cost) i+3j+(5 – 2 sin t) k | traces out a circle in 3-space as t varies. De- termine the radius and center of this circle.

Q: Let r(t) = (-5t5 - 3, 4e-4t, 5 sin(2t)) - Find the unit tangent vector T (t) at the point t = 0.…

A: Given vector  r(t)→=<-5t5-3,4e-4t,-5sin(2t)>

Q: Find the tangent plane to the equation z = 6e* – 2y at the point (4,8,6) - II

A:

Q: The directional derivative of x,y) - 16/x - 13y at the point (11,8) in the direction of the given…

A: The direction derivative  of f(x,y) in the direction of unit vector, is defined as follows.

Q: Sketch the curve of the vector function r(t) = 3ti+ (3t + 1)j,-1<ts2, and indicate the orientation…

A: The given curve in vector form: r(t)=3ti+(3t+1)j The point of t is -1≤t≤2 To find the curve at the…

Q: Find the parametric equations of the tangent line to the curve represented by the vector function…

A:

Q: Suppose you are given a vector-valued function modelling the velocity of a particle in space. At…

A:

Q: Find an equation of the plane tangent to the graph of g(r, y) = 3ev²-z² at the point where (x, y) =…

A:

Q: how would I find the domain of the vector function r(t)=cos(t)i+ln(t)j+1/(t-4)k?

A:

Q: Find the vector equation of the plane tangent to the surface z = x^3 - y^3 at the point (0,1,-1)

A:

Q: At time to, a moving particle has the velocity vector v = 7i and the acceleration vector a = 7i +…

A:

Q: Sketch the curve parametrized by r(f) = (1 – 12, 1) for -1sı<1. Compute the tangent vector at i = 1…

A: Let's first draw the curve -  Domain - -1 ≤ t ≤ 1 where, we can take values of t as -  t = -1, -0.5,…

Q: Represent the plane curve by a vector-valued function. x- + y2 = 4 r(t) = 2 cos ti +2 sin tj

A: x2 + y2 = 4 x2 + y2 = 22 = r2 Therefore, r = 2

Q: Sketch the graph of 7(t) = sin(t)i – 2cos(t)j–tk in 3-space; then find and draw the tangent vector…

A: Given, r→t=sinti^-2costj^-tk^

Q: For the function f(x,y)=x^3−2x^2y−y^2−y, which vector is normal to the level curve at the point…

A:

Q: Find the vector equation of the tangent line to F(t) = (2 sin 2t, cos 2t, – 6t) at the point where…

A: Consider the given vector. rt=2sint,cos2t,-6t   Find the derivative of the vector with respect to t.…

Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: The function is given as f(x,y)=5xy . The point is x=2 and y=8 inclined at angle θ=π3. The…

Q: Find the directional derivative, Dvf , of (*) f(x, y, z) = 4x tan 1 at the point P = (1, 1, 1) in…

A: To find the directional derivative of f(x,y,z) at P=(1,1,1) and the Direction, v=(1,2,2).

Q: Find the tangent plane to the equation z = 2x – 3y + y at the point (1, 2, – 8). -

A:

Q: A point, p, is moving with acceleration 6t j -k at time t. If at t 1, the coordinates of P are (1,…

A:

Q: Find a vector equation for the tangent line to the curve 7(t) = (5 cos(6t))i + (5 sin(6t)) j +…

A:

Q: Find the directional derivative Duf(P) of f(x, y, z) = x²y?z²at the point P(1, 2, 3) in the…

A: We have to find the directional derivative of f(x,y,z).

Q: The vector function r(t) (5 – 2 sin t) i+ (3+2 cos t) j+ 2k traces out a circle in 3-space as t…

A:

Q: 2. Find thé moving trihedral of the curve C traced by the vector-valued function R(t) 4 cost i+4…

A:

Q: x-1 y-2 z-1 2 -6 7 1 F(t) = ( 21 + ¹ )i + ¹/ (m² − 3)} j + t√21³-1k at t=1 1 4 (c) show that the…

A:

Q: Find the point on the graph of z = 3x2 + y at which vector n = (24, 2, –1) is normal to the tangent…

A:

Q: 10. Draw the graph of the vector-valued functions (a) for the plane curve, r(t) = 2cost³i + 3sint³j,…

A:

Q: Find the vector equation of the tangent line to the curve given by 7(t) = sin ti + cos (2t)j + tan…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Find the unit vector towards the tangent of the curve y = x at x =1

A:

Q: Find the point on the graph of z = 3x2 – 2y? at which vector n = (-12, –16, –2) is normal to the…

A: Shown below

Q: Find the vector r' (to); then sketch the graph of r (t) in 2-space and draw the tangent vector r'…

A:

Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (cos(t), sin(3t), cos(3t))…

A:

Q: Find the directional derivative of the function f(x, y) = 2x2y + 6xy at (1, 1) in the direction of a…

A:

Q: Find the equation of the plane tangent Z = (x+2)*- (y-1)²-5 at (2,3,3) to

A:

Q: Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t…

A:

Q: The vector parametric form of the tangent line to r(t) = (3t², ¿, t – 1) at t = -5 is

A:

Q: Find the directional derivative of the function f(x, y,z) =x-y+2z at the point P(1,2,3) in the…

A: Note:- Let a function f(x, y, z), then Direction Derivative of the function f at point P in…

Q: Find a vector function that represents the curve of intersection of the paraboloid z=7x^2+5y^2 and…

A:

Q: At which point P of the curve defined vectorially with r (t) = (21, 4t + 1, t) is the tangent vector…

A: The general form of the parametric equation of the curve in three dimensional space is given by…

Q: A bee with velocity vector r' (t) starts out at (2, 5, -2) at t = 0 and flies around for 1 seconds.…

A: We can answer first question as per the honor policy. Please resubmit other parts as well to know…

Q: A particle moves through 3-space in such a way that its acceleration is a(t) = 8sin 2ti +8 cos…

A:

Q: Show that the vector-valued function r(t) = ti + 2t cos tj + 2t sin tk lies on the cone 4x2 = y2 +…

A: Given: Vector-valued function: r(t)=ti^+2tcostj^+2tsintk^ Cone: 4x2=y2+z2

Q: Find the parametric equations of the tangent line to the curve represented by the vector function 7…

A: Topic  = Vector

Q: Find a unit vector that is normal to the level curve of the function f(x, y) = 5x + 6y at the point…

A:

Q: A curve is given by the parametrization r(t)= [²,-t, ť ]. If the tangent vector to this curve at a…

A: The given curve is,  ,

Q: Find the vector equation of the tangent line to 7(t) = 2 (e1 %3D

A:

Q: Compute the unit binormal vector and torsion of the curve r(t) = (8t, 5 cost, 5 sint (5, 8 sint, -8…

A:

Q: Find a vector function that represents the curve of intersection of the surface 4x+2y-8z^2=16 and…

A: To find a vector function that represents the curve of intersection of the surface 4x+2y-8z2=16 and…

Q: In R', Find the unit vectors that are parallel to the tangent line to the curve y = 2 sin x at the…

A:

Q: The position vector in the xy plane is [t2,sin(t)].  What is the distance traveled by the particle…

A:

Q: 4. If a particle moves in the xy-plane so that at time t its position vector is sin 31 ,3r2 find the…

A: