Let P = (1,3) and Q = (2,6) be points in the plane. Find a vector-valued function R(t) = R0+tv such that R(t) describes the line through P and Q.

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

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Q: Let A(5, -1, -3) and B(1, 3, 2) be two points in R. The directional derivative of f(x, y, z) = xy…

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Q: Find the domain of the vector-valued function

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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 the real values of ,a,b,c that make the convolution equal to zero for the vector function F(x,…

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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 = 16 r(t)

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

Q: Let f(x, y) = x²y'. At the point (-1, 2), find a vector (a) In the direction of maximum rate of…

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Q: Use Theorem 12.10 to find a, and a, for each curve given by the vector-valued function. (a) r(t) =…

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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: Consider the vector function r(t)=⟨t,t7,t5⟩r(t)=⟨t,t7,t5⟩ Compute ⟨r′(t)=⟨  ,  ,  ⟩⟩ ⟨T(1)=⟨  ,  ,…

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Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (a) If Ř(0) = (-1,4,-5),…

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Q: Show that this curve y represents the vector (1,0) as v = 1- +0- in the sense that, for an arbitrary…

A: Given that γ(t)=(t,t2)in R2, t∈[-1,1] The objective is to show that curve represents the vector…

Q: Compute the directional derivative of the following function at the given point P in the direction…

A: NOTE: Refresh your page if you can't see any equations. . the given direction is  find the unit…

Q: Find the point A (a, a, 0) on the line y = x in the xy-plane, such that the vector AB is…

A: Solution is given below:

Q: Find a vector function r(t) that represents the intersection of the surfaces: z = x² + y² z = y + 1

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Q: If Ū is a unit vector and Di f(x, y) = 0 for all points (x, y) then f is a constant function..

A: We have to determine whether the following statement is true or false : If U→ is a unit vector  and…

Q: Let F = 3 x R, where is a constant vector. Calculate F. dR C on the line segment C connecting (1, 3,…

A: According to the given information, it is required to calculate the integral.

Q: Find the real values of a,b,c that make the convolutio equal to zero for the vector function F(x, y,…

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Q: Find the domain of the vector-valued function r(t) = ln ti − et j − tk

A: Given function is r(t)= ln(t) i - etj -tk

Q: Create a graph of the vector-valued function ř(t) = (t² – 1)i + (2t – 3)j, – 3 <t< 3. %3D

A: Introduction: A parametric equation is one in which the dependent variables are defined as…

Q: Make all obvious simplifications.

A: We have to solve

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 gradient vector, Vf, for the function, f(x). f(x, y) = x²y² + ex²y b. f(x,y,z) =x²y*…

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Q: Determine the divergence of the vector: V = i(x2) + j(-xy) + k(xyz) at the point (3,2,1). A) 11.00…

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Find a function f (x, y, z) such that ∇f is the constant vector〈1, 3, 1〉.

A: It is given that, ∇f=&lt;1,3,1&gt;   It is known that a vector ai^+bj^+ck^ can also be represented…

Q: Find the domain of the vector-valued function. (E r(t) = V 25 - t2i + t²j - 2tk tj- 2tk

A: Solution by using definition :

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

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Q: Find the domain of the vector-valued function                                               r(t) =…

A: Given, F(t) = ln ti + 5tj − 3t2k,          G(t) = i + 4tj − 3t2k

Q: Suppose that ∇ƒ(x, y, z) is always parallel to the position vector x i + y j + z k. Show that ƒ(0,…

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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: (a) Find the domain of the vector function r(t) and sketch its range, where r(t) = (v25 – t², 1, vf²…

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Q: Determine whether or not the vector ficld F (r, y, z) = (2ry22, 3ry2, 2ryz) is conservative. If it…

A: The general form of a vector-valued function in three dimensions is given by F=F1,F2,F3, where F1,…

Q: Find the value of h for which the vectors are linearly dependent

A: The given vectors are 1-14 , 3-57 , -15h The vector v3 are linearly dependent if the equation…

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

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Q: Is the vector valued function continuous at t=3? Defend your answer. I² -9 t- 3 V3t – 1, In(4 – t),…

A: Topic = Continuity

Q: Why is r(t) = ⟨ƒ(t), g(t), h(t)⟩ called a vector-valued function?

A: Given r(t) = ⟨ƒ(t), g(t), h(t)⟩. We need to give reason why r(t) is called vector-valued function.

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

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Q: Find the derivative of the vector function r(t) = ta x (b+ tc), where a = (4, -1,5), b = (-3,-3,-1),…

A: Given, the vector function      r(t)=ta×(b+tc),where       a=4,-1, 5, b=-3,-3, -1, and  c=1, 2, 2,…

Q: Consider the vector-valued functions æ1(t) = 5t + 6 and æ2(t) = 3e-2t 8t2 + 3t) 3e-2t

A: In this question, we have to find the wronskian and the interval for the existence of linearly…

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

A: The objective is to find the vector function that represents the curve of intersection of the two…

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

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Q: For a scalar function f(x, y, z) = x? + 3y2 + 2z?, the gradient at the point P(1, 2, - 1) is

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Q: Let T R2 R2 be a linear transfor [3] into the vector a (i) T maps vector u

A: Introduction: A linear transformation could be a operation from one vector area to a different one…

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

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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.

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.