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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: represent the plane curve by a vector- valued function. (There are many correct answers.) y=(x-2)2

A: We have to represent the plane curve by a vector- valued function y = (x - 2)2

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 unit vector that is parallel to the line tangent to the parabola y = x2 at the point (6, 36).

A: The parabola y = x2 and the point (6, 36)

Q: .3 At which point P does the curve r(t) = ( 2t have the tangent vector (24, -8, 3) ? (a) P(2, 2, 2)…

A: Here we have, the given curve is r→(t)=2t3, 2t2, 3t-1                now differentiate with respect…

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: Q1/ If f(x,y)=find a unit vector u for which Duf (2,3) = 0 x+y

A: We have to find a unit vector u for which Duf(2,3)=0 where f(x,y)=yx+y

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

A:

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 the directional derivative of f(x,y)=yln(x+y) at the point (-3,5) in the direction of 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: Find the domain of the vector function. (Enter your answer using interval notation.) r(t) = (V9 -…

A: In the question it is asked to find domain of the vector function r(t)=<9-t2,e-3t,ln(t+2)>.

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: Evaluate, don't forget the constant vector, (ri - 2tj + k) dt

A: We have to evaluate the integral: ∫t2i-2tj+1tkdt We know the formula of integration,…

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

A:

Q: Represent the parabola y = x2 + 1 by a vector-valued function

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Q: Find the domain of the vector tunction. (Entar your answer using interval notation.) r(t) = (V/25 -…

A: " Since you have asked multiple questions we will solve first question for you. If you need the…

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: 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: (b) part of parabola y = −2x² from (−1, −2) to (2, —–8)

A: Given Equation of parabola y=-2x2 from -1, -2 to 2, -8.

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

A:

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

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Q: Represent the plane curve by a vector-valued function. (There are many correct answers.) 4x + 5y −…

A:

Q: C:r=r(t)=(1+t,2 – 3t, 4t)

A: We Have :— X = 1 + t Y = 2 — 3t Z = 4t

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: What is a general equation for the line with vector equation x=[31]+t[4−5]

A:

Q: Find a vector normal to the plane with the given equation.3(x − 4) − 8(y − 1) + 11z = 0

A: Consider the equation of the plane: 3x-4-8y-1+11z=0.   If equation of the plane has the form:…

Q: The path of a particle is moving in the plane with position vector . What is the speed of the…

A:

Q: Find a vector-valued function whose graph is the indicated surface. The cylinder 9x2 + y2 = = 81…

A:

Q: Ex:- Find the directional derivative of fOxy,2) =X-xy-7 atRC,1,0) in the direction of vector A=21-33…

A: Solution is given below:

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: 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: x² + y? Find a vector function that represents the curve of intersection of the paraboloid z = and…

A: Given curves are the paraboloid z=x2+y2 and the cylinder x2+y2=4

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

A:

Q: Represent the plane curve by a vector- x² + y? = 4 r(t) = Need Help? Watch It Read It

A: Representing a curve by a vector valued function means we have to write it's parametrization form.…

Q: Represent the plane curve by a vector-valued function. x² + y² = 36 r(t) = (No Response) Need Help?…

A: The plane curve x2+y2=36

Q: Q2) Find the vectors „N of the curve r(1) = ) at the point (1.1)

A:

Q: 2) r(1) = ti –t j-tk, t20 Draw the graph of the vector-valued function, explaining it in detail.

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

Q: a) Start by finding a single vector function that represents the intersection of the surfaces z = y?…

A: Given: The two surface equation: z = y2 and  x2 + y2 = 4

Q: E Explain how the vector V= (0.6, 0.8, -2) can be thought of as having a "slope" of-2. %3D

A: Please check step 2 for the solution.

Q: Give a set of parametric equations for the line L4 that lies tangent to the graph of the vector…

A:

Q: Sketch the graph of the vector-valued function F(t) = (2t – 1)² î +(2t +2) ĵ. Draw arrows on your…

A: The vector valued functions in two dimensions can be represented as r→(t)=x(t)i^+y(t)j^.

Q: If two objects travel through space along two different curves, it's often important to know whether…

A: To solve this we must figure out at what t's positions are equal for each vector component. so, set…

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 the domain of the vector-value function r(t) = www Domain: {tt # MORA 4t4, t², 1 (t - 2)5

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Q: Q1\ Explain with short examples the algebraic vector properties.

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.