Graph the curve traced by the given vector function r(t)=ti +2tj+costk;t>0.

Q: Represent the plane curve by a vector-valued function. x2 /16−y2/ 4= 1

A:

Q: Represent the plane curve by a vector-valued function. r(t) =

A: Let's represent the plane curve by a vector valued function.

Q: Sketch the graph of the plane curve . r(t) = ti − t3j and sketch the vectorsT(t) and N(t) at the…

A: Here we are taking the T(t) as the tangent vector and N(t) as the Normal vector Consider the…

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

A: To indicate the direction in which t increases and sketch the graph of the vector function given…

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

A: Topic = vector

Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: Given:

Q: An object moves in a path defined by the vector-valued function r(t) = 4tî +t²j, wheret measures…

A: Using formula of aT and aN solve it.

Q: Find the derivative, r'(t), of the vector function. r(t) = tan(8t), sec(4t),

A:

Q: Given the vector-valued function r(t) =

A: Given  r→(t)=cost,3t,2sint

Q: Sketch the curve represented by the vector-valued function                              r(t) = (t +…

A: Given: The vector-valued function  r(t) = (t + 1)i + (3t − 1)j + 2tk and it gives the orientation of…

Q: Represent the plane curve by a vector-valued function. x2 + y2 = 16 r(t)

A: The given plane curve is   x2+y2 =16.  We have to represent the curve by a vector valued function…

Q: If is a smooth curve given by a vector function r(t) a < t < b and is a constant vector, show…

A: So we have;

Q: The curve with vector equation r(t) = t'i + 2tj+ 3tk is %3D a line.

A:

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: Find the derivative of the vector function r(t)=ta×(b+tc) where a=⟨−4,−3,5⟩ b=⟨−1,2,5⟩ and…

A: Solved below

Q: A space curve is given by the vector function r(t) = (3t, t² + 6t, t³ ). Then the unit tangent…

A: GIVEN: r(t) = {3t, t2 + 6t, t3}

Q: Find the derivative, r'(t), of the vector function. r(t) = ( tan(2t), sec(5t),

A: We have to find the derivative of the given vector function  r(t)=< tan(2t) ,sec(5t) , 1/t^3>…

Q: Find a vector equation for the tangent line to the curve 7(t) = (8t²) i + (3t – 2) 5 + (8t³) k at t…

A:

Q: find the dot product of a vector function with itself. r(t) is a curve and the magnitude of r(t)=pi…

A: Let  u = a i^ +b j^ be a vector functionthe dot product of u with itself is given byu·u = a i^ +b…

Q: Sketch the curve represented by the vector-valued function                               r(t) = 2…

A: Given information: Vector-valued function rt=2costi+tj+2sintk trigonometric identity, sin2t+cos2t=1…

Q: Again just working on examples for exam, would like to see how you solve this to see if it is the…

A:

Q: The graph of the vector function r (t) = 2i + t²j+ tk is

A: Given function is r^t=2i^+t2j^+tk^. Plot the graph of the vector function. Choose some values for t…

Q: Sketch the path of an object moving along the plane curve given by                  r(t) = (t2 − 4)i…

A: To sketch the path of an object moving along the plane curve given by r(t)=(t2-4)i+tj To find the…

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

A:

Q: Find the derivative of the vector function r(t) = In(13 – t²)i+ y13+tj– 9e 3 k r'(t) = {

A: The given vector function is                                   r(t)=ln13-t2i+13+tj-9e-3tk

Q: Find the tangential and normal components of the acceleration vector for the curve F(t) = (t²,…

A: Here we have to find the tangential and normal components of the acceleration vector for the curve…

Q: Match the vector-valued function with its graph. r(u, v) = u cos(v)i + u sin(v)j + uk

A:

Q: The graph of the vector function r(t) = ti +t²j+2k is

A: Graph of vector function  r(t) is :  r(t)= t i + t2 j + 2k

Q: Give the length of a curve given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in…

A: given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in the vector form.

Q: Represent the plane curve by a vector-valued function. x2 + y2 = 36 r(t)

A: Represent the plane curve by a vector- valued function                       x2 + y2 =…

Q: ). Determine the set Tp(Zf) of all tangent vectors to Zf at p. Is dim Tp(S) m ker d f.?

A: Sol

Q: Find the unit tangent vector to the curve defined by =(- 4t, 4t, V49 - t) at t = - 6. T(- 6)

A:

Q: Represent the plane curve by a vector-valued function. x2 + y2 = 25

A: It is given that, x2 + y2 = 25. Let x=5cost and y=sint , Then 5cost2+5sint2=25cos2t+sin2t=25

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

A:

Q: Match the vector-valued function with its graph. r(u, v) = ui + vj + uvk -2-1 2 2

A:

Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: First solve the given equations for finding the values in terms of x

Q: The graph of the vector functionr (t) = 2i +tj+tk is

A: 3d graph related problem.....

Q: Find the derivative, r'(t), of the vector function. r(t) = (e-t, 6t – t3, In(t))

A: Solution-  Given vector function  r(t) = (e-t, 6t-t3, ln (t)) We have to differentiate these…

Q: Compute the unit binormal vector B for the following parameterized curve: F(t) 4 2 3t, 1

A: Given:    r(t) = ⟨ t2/2 , 4-3t , 1 ⟩

Q: Sketch the curve whose vector equation is r(t) =

A: given rt=<tcost,tsin,t>

Q: Find the derivative, r'(t), of the vector function. r(t) = (e-t, 4t - t, In(t) r'(t)

A:

Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A:

Q: B- Find the length of the curve given by the position vector r=, =r'i+(1+(1/3)x')j+(1-(1/3)')k for

A:

Q: sketch the curve represented by the vector-valued function and give the orientation of the curve.…

A:

Q: Find the point on the graph of z = 3x2 – 3y? at which vector n = (48, –60, –2) is normal to the…

A:

Q: Sketch the curve with the vector equation 7(t) = (t,2 – t, 2t). Indicate with an arrow the direction…

A: Solution

Q: Sketch the plane curve represented by the vector valued function and give the orientation of the…

A: Given rt=t3i+t2j.

Q: Sketch the curve of the vector function r(f) = ti +4costj, and indicate the orientation of the…

A: We have to sketch the curve of the vector function rt=ti+4costj, and to indicate the orientation of…

Q: Find the tangent vector of r(t) = (t° , 3tª) at time t = 1. A) (3, 12) B) 15 C) (3, 7) D) 3t2 + 12t3

A:

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.