Find a vector function r(t) that describes the curve of intersection be- tween the elliptical cylinder 4y² + z² = 4 and the plane x + y = 1. Sketch the curve of intersection by skecthing the two surfaces.

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

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

A: To find :               Find the vector valued function whose graph is the indicated surface.

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

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

A: Given:

Q: Find both the parametric and vector equation of the line segment between (−2, 3) and (5, −1) where 0…

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Q: Find a vector parametrization of the curve x = -3z² in the xz-plane. t as the parameter in your…

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Q: Find a vector tangent to the curve of intersection of the two cyclinders x2+y2=32x2+y2=32 and…

A: Solution: The objective is to find a vector tangent to the curve of intersection of the two…

Q: Find a vector parametrization 7 (t) for the intersection between the two surfaces: x² + 10y4 + 223 =…

A: According to the given information, it is required to find a vector parametrization for the…

Q: A particle moves in a path defined by vector-valued fanction FH)= (4)i +(zt-3)j + ( 3t - 3t) K ,…

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

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Q: Represent the plane curve by a vector-valued function. y = (x − 2)2

A: y=x-22 Now let xt=t Now put xt=t in y=x-22, we get y=t-22

Q: Consider the curve C parameterized by f(t)=(t^2+2t+3,-2t-4,t^2-1),t E [0,+infinite[ a)Find the plane…

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Q: Sketch the curve with vector equation r(t) = (t2 – 2, t) in the xy-plane. Indicate with arrows the…

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Q: Find a vector equation with parameter t for the line of intersection of the planes x + y + z = 4 and…

A: To find the equation of line with parameter t of the intersection of the planes  x + y + z =4 and…

Q: Let C be the upper half of the circle whose equation is x2 + (y - 2)2 that is generated by revolving…

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Q: Find a vector tangent to the curve of intersection of the two cyclinders x2 + y? = 8 and y? + 22 = 8…

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

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Q: Find a vector equation with parameter t for the line of intersection of the planes x + y + z = 3 and…

A: Given plane equations are  x + y + z = 3 and x + z = 0. We have to find the intersection line…

Q: Find a vector normal to the surface 3z 3 + x 2 y - y 2 x = 1 at P =(1,-1,1) .

A: Given: 3z3+x2y-y2x=1 at P(1,-1,1)

Q: Represent the plane curve by a vector-valued function y=1-x^2

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Q: Determine the vector equation that represents the curve of intersection between the cylinder 2¹² +…

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Q: Compute the equation of the plane tangent to the surface x^2+3 y^2+z^3 = 8 at the point (2,1,1).

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Q: Find a vector function r(t) that describes the curve of intersection between the elliptical cylinder…

A: given, elliptical cylinder 4y2+z2=4  and the plane x+y=1 we have to find a vector function r(t) that…

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

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Q: Find a vector function that represents the curve of intersection of the cylinder x^2 +y^2 =1 and the…

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Q: Represent the plane curve by a vector-valued function. 2x − 3y + 5 = 0

A: Given: 2x-3y+5=0 for finding given equation in vector form, we assume x=t and find value of y in…

Q: find the points on the surface + z² = 1 that have their tangent plane perpendicular to the vector…

A: For tangent plane of the surface f(x,y,z)=k at a given point normal vector to tangent plane  will be…

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: Find the Vector function that represents the curve of the intersection of the two surfaces.  The…

A: Given equations are x2+y2+4z2=4 ..... (1) and x2+z2=1 ..... (2) From equation (1) z2=(4-x2-y2)/4…

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: Find a vector function that represents the curve of intersection of the two surfaces. The cone y = v…

A: Given data: Equation of cone is y=2x2+9z2. Equation of plane is y=5+3z.

Q: Find a vector equation with parameter t for the line of intersection of the planes x + y + z = 4 and…

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Q: Find the derivo tive of the function flxy)=xy+y2 in the direction of the vector D-j ot the point…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: find an equation for the plane that is tangent to z=4x^2+y^2 at the point (1,1,5)

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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: Choose the normal vector of the tangent plane to the surface defined by z =e4x²+16xy-9y2 at the…

A: Explanation of the answer is as follows

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 curve of intersection of the surfaces, and find a vector equation for the curve in terms…

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Q: Choose the normal vector of the tangent plane to the surface defined by at the point (-4, 2, e88). O…

A: Given problem:- Find the normal vector of the tangent plane to the surface defined by…

Q: Find a vector tangent to the curve of intersection of the two cyclinders x2 +y? = 200 and y? + z2 =…

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Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 2x² + y²…

A: Given: Let us take x = t. So, we get y=t4  and  z=2t2+t42=2t2+t8.

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

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Q: Sketch the curve of intersection of the surfaces, and find a vector equation for the curve in terms…

A: First, we will sketch the curve of the intersection of the surface. The equation of the surfaces are…

Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 4x2 + y and…

A: The given curves are: z=4x2+y2     and     x=ey

Q: What is the perpendicular vector to the surface f(x.y.a)-ay-3r+'y-0 at (1,-1,2)? (3,3.0) (1,1.3)…

A: A vector that makes an angle of 90 degrees with the given surface is said to be perpendicular to the…

Q: Find a nonzero vector normal to the plane z−3(x−4) = −4(1−y) correctly.

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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: Represent the plane curve by a vector-valued function. y = x + 5

A: To Determine: represent the plane curve by a vector function . Given: we have a function y=x+5…

Q: Find a vector function that parameterizes the curve of intersection between the surfaces y^2-z^2=x-2…

A: To determine the vector function for the curve of intersection between the surfaces.

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.