How do you find the length of a space curve given by a vector function r(t)

Q: Represent the plane curve by a vector-valued function. y = 3 – x² r(t) = %3D

A: Represent in general expression

Q: vector furm : r(t) = ro

A: To represents the equation of line in space ,  The coordinates are  x0, y0 ,x1,y1. a. To represent…

Q: Prove the parallelogram law on an inner product space V; that is, show that ||x + y||2 + ||x −y||2=…

A: Consider the given identity of parallelogram law on inner product space. Using distributive law…

Q: Represent the plane curve by a vector-valued function. (There are many correct answers.)

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Q: A person on hang glider is spiraling upward due to rapidly rising air on a path defined by x²/9…

A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: Find the equations of the normal line and the tangent plane to the parametric surface defined by the…

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Q: Fine the Vector function that represents the curve of intersection of the two surfaces. The cone z=…

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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: Verify Stoke's theorem for the vector point function yz2 (xz² .3 + ex over the surface S of the cube…

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Q: Q and Z are vector valued functions Q(-1) = , Q'(-1) = , Q''(-1) = Z(-1) = , Z'(-1) = , Z''(-1) =…

A: Given Q and Z are vector valued functions such that:Q-1=0,0,-2Q'-1=1,-1,-1Q''-1=3,2,-2 and…

Q: Determine whether the statement is true or false "If a particle moves along a sphere centered at the…

A: The given statements is “If a particle moves along a sphere centered at the origin, then its…

Q: 1. True or False: It's possible for the directional derivatives of a given function along two…

A: Solution-1)

Q: Find a vector-valued function whose graph is the indicated surface. the ellipsoid   x^2/1 + y^2/8 +…

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Q: ind the directional derivative of the function f(x, y, z) = Vx² + y² + z² at point (2, -3, 6) in the…

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Q: Let z = f(x, y) be a differentiable function defined for every point on the plane, and let u be a…

A: (a)Let the function f(x,y) be the height of a mountain range at each point X =(x,y). If you stand at…

Q: sketch the space curve represented by the intersection of the surfaces. Then represent the curve by…

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Q: Sketch the space curve. Vector-Valued Function r(t) = -ti + 6tj + 5tk 2 -2 5 0 y Z Z 2 5 Find its…

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Q: Find a vector parametrization of the curve x=−2z^2 in the xz-plane. Use t as the parameter in your…

A: Find a vector parametrization of the curve x=−2z^2 in the xz-plane. Use t as the parameter

Q: ia vector-valued function whose graph The ellipsoid 9 = 1 49

A: r(u, v) = 3 sin(u) cos(v) i^ + 7 sin(u) sin(v) j^ + cos(u) k^

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

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Q: Example: find the tangent plane and normal line of the surface f(x, y, z) = x +y² +z² = 3 at the…

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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 y = 9 − x2

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

Q: Find a unit normal vector to the surface 6x2 + 2y2 + z2 = 225 at the point P : (5, 5, 5), and…

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Q: Find Frent formulas for a differentiable regular curve a = a(s), then show that at every point on a…

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Q: cise 1.10. (a). Let V = R² = {(x,y)| x,y 2 0} with usual addition and scalar multiplication. Is it a…

A: Multiple:   Let , V = ℝ2 = x , y | x , y ≥ 0. We need to show that , V is a vector space or not. We…

Q: Sketch the space curve. Vector-Valued Function r(t) = -ti + 2tj + 6tk ** kk Find its length over the…

A: Given problem:- rt=-ti+2tj+6tk , [0,1]

Q: (a) Find the direction for which the directional derivative of the function f(x, y) = 9xy + 2y is a…

A: Formula for directional derivative Du→fP=∇f(P).u^=∇f(P)u^cosθ Du→fP to be maximum angle θmust be 0.…

Q: Example: find the tangent plane and normal line of the surface f(x, y, z) = x + y' +z-9=0 at the…

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Q: Sketch and describe the curve defined by the vector-valued function below. 7(t) = (t cos t, t, tsin…

A: To sketch: The curve r(t)→=<tcost,t,tsint> Solution: Given x=tcost,y=t,z=tsint…

Q: Consider the family of curves y I 1+ GI

A: We have y=x1+c1x Differentiate with respect to x: dydx=ddxx1+c1x⇒dydx=1+c1xdxdx-xd1+c1xdx1+c1x2…

Q: How do you define and calculate the velocity, speed, direction of motion, and acceleration of a body…

A: To define and calculate the velocity, speed, direction of motion, and acceleration of a body moving…

Q: A particle moves in the xy− plane according to the law x=at, y=bt2, where a>0, b>0. Determine…

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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: Example: find the tangent plane and normal line of the surface f(x, y, z) = x + y° +z-9=0 at the…

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Q: A sphere is inscribed in a straight circular cylinder. The sphere is cut by any two planes…

A: Now we will place the sphere at the origin and the cylinder  with the z-axis as it's central axis.…

Q: 5. Suppose that we have a function f(x, y) and a point P = (a, b) in the domain where ) and = 0.…

A: Given that for the multivariable function f(x,y) , ∂f∂x=0 & ∂f∂y=0  at P=(a,b).

Q: Let the space curve be the intersection of two surfaces z = x² + y² and y² + z² = 1. Draw this curve…

A: As per the question we are given two 3d surfaces defined by the equations : z = x2 + y2   ;   y2 +…

Q: Let f be differentiable function then then the quantity Vf · û where û is a unit vector is maximized…

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Q: ATA, B curi(A x B) = A (div B) – B (div A) + (B-V) A - (A.V) B, are two differentiable vector point…

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

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Q: Find the space curve represented by the intersection of the surfaces. Then represent the curve by a…

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Q: Let u be the vector vith initial point P(5, -3) and terminal point Q(-1, 4). (a) Graph u in the…

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Q: Write a function from r ^2 to r that has a plane with normal (1,1,1) exactly one point.give an…

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Q: The force exerted by an electric charge at the origin on a charged particle at a point (x, y, z)…

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Q: Give a vector valued function (see image 1) that traces out the line but does not use arclength as a…

A: A vector valued function or a vector function for a 2-D plane is given by,…

Q: 4. (8 points) Find a vector parametrization for the intersection of the plane x +y+z = 3 and the…

A: Use polar coordinates for Parameterization

Q: ). The force exerted by an electric charge at the origin on a charged particle at a kr where k |r]3…

A: We have to find the work done from moving the partical.   It is basically a dot product problem from…

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.