t 0.5 1.0 1.5 2.0 2.5 3.0 Speed

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

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Q: Find the directional derivative of the function f(, y) = In(x + y°) at the point (- 1,3) in th…

A:

Q: The natural domain of a vector-valued function is the intersection of the domains of its component…

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Q: The acceleration of an object after t seconds is given by the vector-valued function a(t) . | If…

A: to find the velocity equation, take integration  .............(1)

Q: What is the zero vector?

A: We have to define

Q: Find a vector equation with parameter t for the line through the points (–1, –7, –4) and (-9, 8, 2).

A: we know that vector equation of line which passes through pointsx1,y1,z1,x2,y2,z2 is given by…

Q: What is meant by a tangent vector?

A: To Explain:  a tangent vector

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: Suppose that r1(t) and r2(t) are vector-valued functions in 2-space. Explain why solving the…

A: It is given that r1(t) and r2(t) are vector valued functions in 2-space. The objective is to explain…

Q: Show that the graph of the vector-valued function r(t) = is a circle, and find its radius and…

A: The equation of a circle is defined by the equation, (x-h)2+(y-k)2+(z-l)2=r2 , where, (h,k,l) is the…

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

A:

Q: An object moves with velocity vector (t,t?,-t) starting at (1,2,3) when t=0. Find the function r…

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

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 the x-component of the vector of length 3 in the direction of V = (-1,-1).

A: v=<-1,-1>=-i-j Unit vector in the direction of vector V i.e.,     v⏜=-i-j(-1)2+(-1)2 =-i-j2…

Q: Q3/A- Show that for any position vector r the binomai vector B is always orthogonal to the…

A: We have to solve given problems:

Q: Find the directional derivative of f at the point (1,2) in the direction of the vector v = = (1, 3).

A:

Q: A vector whose initial point is at the origin is called a/an________ vector.

A: Consider the given: A vector whose initial point is at the origin is called a/an________ vector. A…

Q: 6. A payload is launched from a plane at altitude 3000 meters with an initial horizontal and…

A: t           = time of flight since payload is dropped in seconds 3000m = the height of the payload…

Q: (a) Find the directional derivative of the function f(x, y) = 4.xy – x2 – y? in the direction of…

A:

Q: 8. Find the scalar equation of the line passing through the point (1, 5) that has a normal vector…

A:

Q: Express the unit vector directed toward the origin from an arbitrary point on the line described by…

A: solution : Given the point x=0, y=3 and z1.22unit vector is defined…

Q: Find the directional derivative of in the direction of the vector (1,3) at the point (-1,2)

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Q: 7(t) =

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

A:

Q: 3. A hiker begins at the origin and walks in a straight line in the direction of the vector (1,1)…

A: 1st we have to find points where hiker changes its direction and then draw figure of path  Distance…

Q: Find the unit vectors that are parallel to the tangent of the polynomial y= x^3 +2x + 1 at the point…

A: Consider the given function and differentiate to get the slope of the tangent.

Q: The natural domain of the vector-valued function  is

A:

Q: Find the two-unit vectors that are parallel to the tangent line to the curve y =x2sin(x) at the…

A:

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 that gives the direction of maximum rate of increase for the 6xyz at (-1,2,1) (a)6(2i…

A: To find A vector that gives the direction of maximum rate of increase.

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

A:

Q: (b) Identify the unit vector ū pointing in the direction of maximum increase of the function f(x, y)…

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Q: (a) What is the maximum directional derivative of g(x, y) = y²e2¤ at (2, – 1) and in the direction…

A:

Q: Find a vector equation for the line that goes through the points (7, 6, 2) and (2, 14, 2). F(t) =…

A: Given: Let A(7,6,2) and B(2,14,2) be the two points the line passes through To find: vector equation…

Q: Q3: Find the scalar and vector components of the vector with initial point (2, 1) and terminal point…

A: Given initial point A(2,1) and terminal point B(-5,7)

Q: ) Find a vector equation for the line that goes through the points (7, 6, 2) and (2, 14, 2). F(t) =…

A:

Q: Calculate and display the error vector & and use it (c) to provide an orthogonality check on your…

A: Given: The set of data points, x y z 0 0 4 1 0 4 0 1 4 1 1 0 To plot them on a set of…

Q: Given the vector-valued function

A:

Q: Match the vector valued function with its graph where 0 <t < 2n. Not all equations will be used. Use…

A:

Q: What is special about the derivatives of vector functions of constant length? Give an example.

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Q: (B) At point (1,5), Find the Vector that is tangent and Normal to the curve: X' = 2y + 10

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Q: Find the directional derivative of the function f(r,y) In(z +y") at the point (2, direction of the…

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Q: the vector-valued function.

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Q: A vector with magnitude 4 points in a direction 265 degrees counterclockwise from the positive x…

A: Given  Magnitude of 4 points at an angle of 265° In counter clockwise direction  from positive x-…

Q: a) Determine the gradient for the vector A = 4x'yz+ x²y²z² at point (2,-2,3) travelling %3D along in…

A: Given: A=4x2yz+x2y2z2 at point (2,-2,3)

Q: Find the directional derivative of the function f(x, y) = x²y° in the direction of the vector at…

A: Concept:

Q: Calculate the directional derivatives of the function f(x,y) = x² – y? in the direction of the…

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Q: If g(x,y) is equal to the equation given and point P(1,1), express the domain of g as a set and…

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.