Find a vector function that represents the curve of intersection of two surfaces: z = x² - y? and x² + y² =1

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. 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: Find a vector parallel to the line of intersection of the planes 2x + 3y – z =11 and 4x + 2y – 3z =…

A: We need to find a vector parallel to the line of intersection of the planes 2x+3y-z=11 and 4x + 2y -…

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

A: Given:

Q: Find a vector n normal to the plane with the equation 5x - 5y – z = 10. n = (5,

A: Given equation of plane is 5x-5y-z=-10.want to find:Normal vector n to given plane.

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

A:

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: 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: Find a vector function that represents the curve of intersection between the paraboloid 2 z = 4x² +…

A:

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

A:

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

A:

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

A:

Q: Two plane curves are defined by the vector functions r1(t)=⟨t,2t−4⟩ and r2(u)=⟨2u,u2⟩. Find the…

A:

Q: Find the vectorequationof the line of intersection of the planes  2x-3y–z=5 and x+y+2z=1

A:

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

A:

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

A:

Q: Find a vector orthogonal to the line x+y=1

A:

Q: Find a vector function that represents the plane that passes through thepoint p0 with position…

A: The plane passes through the point p0 whose position vector is r0→. The plane also passes through…

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

A:

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

A: The intersecting curve of two surfaces is given as follows:

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: 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: Represent the plane curve by a vector-valued function y = 9 − x2

A: Given:y=9-x2The vector valued function for  a plane curve:rt=xti+ytj

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

A:

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: The separation vector can be written as R = (x – x')ê+ (y – y')ŷ + (z - z')2, Find

A: Given,             R→=(x-x')x^+(y-y')y^+(z-z')z^

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 parallel to the plane 2x - y - z = 4 and orthogonal to i + j + k

A: Given:A plane 2x - y - z = 4 orthogonal to i + j + k

Q: State the difference between a position veetor and a line vector.

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: Find a nonzero vector parallel to the line of intersection of the two planes 5y – 4x + z =-1 and –…

A: The line of intersection of two planes is orthogonal to their respective normals.

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…

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

A:

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: 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.

A:

Q: Find a vector x whose image under T,

A: A=12541022011-4-9-21 ,b=12543-51The augmented matrix of the system is 12541022011-4-9-2112543-51now…

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.

Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: