Usé the parameter x = t to find a vector-valued function for the space curve represented by the intersection of the surfaces x2 + z2 4 and r-y = 0.

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

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Q: 1. Use the parameter r =t to find a vector-valued function for the space curve represented by the…

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Q: sketch the space curve and find its length over the given interval. Vector- valued function:…

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Q: Represent the plane curve by a vector-valued function. y = 3 – x² r(t) = %3D

A: Represent in general expression

Q: Find a vector-valued function whose graph is the indicated surface.

A: In polar coordinates, Using this rule, using appropriate substitutions:

Q: Let C be the curve of intersection of the paraboloid a² + y² = z and the cylinder +(y-1)² = 1 (a)…

A: Given that C is the curve of intersection of the paraboloid x2 + y2 = z and the cylinder x24 + y -…

Q: Sketch the space curve represented by the vectorvalued function                  r(t) = ti + (2t −…

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Q: Let C be the curve of intersection of the paraboloid x² + y² = z and the cylinder + (y − 1)² = 1 (a)…

A: We will use the basic knowledge of vector calculus and differential calculus to answer all three…

Q: Find a vector-valued function whose graph is the indicated surface. The cylinder 9x² + y² = r(u, v)…

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Q: Find a vector-valued function whose graph is the indicated surface.

A: Given : The plane x + y + z = 6.   To find a vector-valued function.

Q: The vector equation for the curve of intersection of the surfaces a = y? and z = y in terms of the…

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Q: Use the parameter x = t to find a vector-valued function for the space curve represented by the…

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Q: Represent the plane curve by a vector-valued function. x² = y² = 4 %3D

A: We have to represent the plane curve by a vector-valued function.…

Q: Verify Stoke's theorem for the vector point function yz2 (xz² .3 + ex over the surface S of the cube…

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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: Sketch the space curve represented by the intersection of the surfaces           x2 + y2 + z2 = 16,…

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Q: Surfaces z = x² + 2y², x + y = 0 X Parameter x = 5t

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Q: f f(x, y, z) = xy: on of vectorî - %3D

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Q: Find a vector function that represents the curve of intersection of the two surfaces. The paraboloid…

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Q: The cone z = x² + y² and the plane z = 1 + y

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Q: Find a vector-valued function, using the given parameter, to represent the intersection of the…

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Q: Find a vector-valued function whose graph is the indicated surface. The plane x + y + z = 2 r(u, v)…

A: Given plane    x+y+z = 2                 this gives   z = 2-x-y            Now, let  x=u    and…

Q: Find a vector that is perpendicular to the surface 4e^{(z-1)}+x^{2}y=xyz at the point (−1,−2,1).

A: Given the surface :

Q: Find all points of intersection between the vector functionr(t) =⟨t, t2, t3⟩ and the plane defined…

A: Since the vector is contained in the plane, so all the points of the line intersect with the plane.…

Q: Let f(r.y) = r'y- Find a unit vector tangent to the level curve f(r, y) = 3 at its point (1,2).

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Q: Sketch the space curve. Vector-Valued Function r(t) = −ti + 3tj + 4tk Interval [0, 1]

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Q: Find a vector parametrization of the curve z = :-222 in the xz-plane. Use t as the parameter in your…

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Q: Find a vector-valued function whose graph is the indicated surface. The plane z = 7y r(u, v) =

A: Given the given surface is z=7y

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: use the parameter x=t to find a vector-valued function for the space curve represented by the…

A: Given surface x2 + z2=4 and x - y=0   and the parameter x = t

Q: Find a vector function that represents the curves of intersection of the two surfaces. 1.- The…

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Q: Match the space curves in the figure below with the following vector-valued functions: O A. r(t) =…

A: See that options ,  A )  r ( t ) = < 1 , t , t >  If we consider the first two coordinates ,…

Q: Find the directional deriu atrue Du f(-3,-1,3) for the function f (xiy,z) =xy + yz +Z X in the…

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Q: Why is r(t) = (f(t),g(t).h(t)) called a vector-valued function? %3D

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Q: Find a vector function, r(t), that represents the curve of intersection of the The cylinder x² + y2…

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

A: We have to find vector function For this we have given equation of paraboloid and parabolic cylinder…

Q: Sketch the space curve. Vector-Valued Function r(t) = -ti + 2tj + 6tk O 5 5 5 * * kk 5 Z Find its…

A: We have to sketch the vector and find the length of curve.

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

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Q: Find a vector-valued function whose graph is the indicated surface. The plane z = 4y r(u, v) =

A: Solution ) the plane      z = 4y   Let's make substitution  x =u , y = v  Hence  z = 4v   r ( u, v)…

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

A: This is a question from Vector Calculus.

Q: ƏF dF = (dr. V)F+ -dt. at

A: Given: A vector function F depends on both space coordinates x, y, z and time t.  To Find:  To show…

Q: Let ƒ(x,y) = x²e"9. Give the unit vector that points in the direction of maximum increase along the…

A: Given that: f(x,y)=x2exy& the point is (x,y)=(1,1)

Q: Find a vector-valued function whose graph is the indicated surface: the part of the paraboloid z =…

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

A: Given rt=t3i+t2j.

Q: find the open interval(s) on which the curve given by the vector-valued function is smooth.…

A: given   r(θ)=(2cos3θ)i+(3sin3θ)j

Q: Consider the vector space of continuous functions over the interval [-1,1] with the inner product…

A: Given that,

Q: dA If A (u)is a differentiable vector function of u and||A (u) || = 1, prove that is perpendicular…

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Q: Describe what it means for a vector-valued function r(t) to be continuous at a point.

A: A vector valued function r(t) which is continues at a point, describes the fact that the limit of…

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.