vetermine aU state the woIK UONE DY the Vector nera over the given path in each situation, F (x,y)= (x-2y,3x) moving from (0,0) to (3,6) to (9,0).

Q: Evaluate along the curve y=x2 from (-1,1) to (2,4). First find the vector valued function r(t)…

A: Curve length problem..

Q: A space turd with velocity vector r' (t) starts out at (-4, 0, 5) at t = 0 and flies around for 5…

A:

Q: 41. The cone z = /x² + y² and the plane z = 1 + y

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

Q: Find a point-normal equation for the plane that is represented by the vector equation (x, y, z) =…

A:

Q: determine the unit vector from which f grows faster in P and determine a rate of change of f in P in…

A:

Q: A fly is moving on the xy-plane along a straight line segment starts at (3,3) and ends at (2,1) Find…

A: In the given question we have to find the path of the fly along the straight line that starts from…

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

A:

Q: An object’s trajectory in 2D has acceleration vector a(t) = ⟨1,1⟩, initial velocity v(0) = ⟨0, 1⟩,…

A: The given data is: at=1,1v0=0,1r0=0,0  To find rt

Q: 3. fimdia a.A. vector.artheogenal.te. xv.and. Txw. b. A vectore.or.thogenal.b. und. SA…

A:

Q: Consider a triange in the second dimension. One vector is fixed at the origin. The other two…

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Q: a) Let i = xî + yj + zk, r = |7| and å is a constant vector. Find the value of %3D dxr div

A: We will find out the required value.

Q: Find a vector valued function which gives the curve of intersection of  y2 + z2 =16  with the plane…

A: Given the curves:

Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (cos(t) , sin(3t) , sin( when…

A: Given r(t)=cos(t) , sin(3t) , sin(t) Compare it with r(t)=x(t) , y(t) , z(t) to obtain…

Q: gravity and wind.

A:

Q: The position vector of a moving particle in space at time t is given by the vector function r (t) =…

A: position vector of particle in space r→(t)=12(5-t)2i→+(2t-1)j→+43(5-t)32k→

Q: (1 point) Evaluate the line integral Sc F dr, where F(z, y, z) = -5zi – yj + 3zk and C is given by…

A:

Q: Find a vector function thet represeds the curve of intersectson of イhe pabeloid Zニx-tye and the…

A: Given, a paraboloid z = x2 + y2 and the cylinder x2 + y2 = 4. We have to find the vector function…

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: r(1) = , 1 > 0. (a) Find the time to > 0 at which the particle crosses the plane x +y 0. (b) At some…

A:

Q: A particle moves so that its position vector r at timet is r = a cos wt + bsin wt, where w is a…

A:

Q: Vector Field: F(x,y) = (1, 0.5 y) and Closed Path: x + y? = 16 Since we do not have our path as a…

A:

Q: Find a vector function that represents the curve of intersection of the cylinder x^2 +y^2 =1 and the…

A:

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

A:

Q: A smooth curve is normal to a surface f(x,y,z) = c at a point of intersection if the curve's…

A: Given: A smooth curve is normal to a surface fx,y,z=c at a point of intersectionif the curve's…

Q: A particle moves in the xy-plane along the curve represented by the vector-valued function r(t) = (4…

A:

Q: Exercise III Let (a) o = x²y +xż and (b) ó = x² + y² + z?. Then, respectively attempt to find the…

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Q: YouTrylt 4 Find a vector function r(t) that parameterizes the intersection of the elliptic cyl 9 4…

A:

Q: Determine a direction derived from the point P and in the direction of the versor vector → informed…

A: In the given question we have to find the directional derivative of the given function. Concept: The…

Q: 3. firmdian .a. A. vector.onthogonal.tr.xv.and.xw. .b.. A. vecter.ortheanal.br. and. Co.…

A: Use the following formulae, to obtain the solution. The vectors u→ and v→ are said to be orthogonal…

Q: Write the equation of the plane with normal vector n=5j passing through the point (2,10,9) in scalar…

A: Give normal vector is:

Q: A. Find a unit normal vector to the surface at the given point. [Hint: Normalize the gradient vector…

A: To find out the unit normal vector to the surface at the given point.

Q: Calculate the line integral of the vector function V (2? – y, y² + æ) from the point (0,1) to point…

A:

Q: A force F acts on a particle that is moving in two dimensions along the semicircle x = 1 – cos 0, y…

A: Given the forces on a particle that is moving in 2D along the semicircle x=1-cosθ, y=sinθ, 0≤θ≤π.

Q: a nonzero vector parallel to the line of intersection of the two planes x + 3y + 5z = -3 and x + 3y…

A:

Q: Q5: Plot the function y= 2 tan(t)-cos(mt) labeling the x and y axes. Where t is a vector containing…

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Q: The acceleration of a moving particle in space is given by the vector function a (t) = 3t2 i + 4t +…

A:

Q: (8) Find a vector parameterization of the line r(t) which passes through the point P = (1,2, –8)…

A:

Q: a) Find the directional derivative f (x, y, z) = x In(y+z) at point P (2, e, e) in the direction of…

A: We have to find directional derivative of vector f in the direction of vector v:

Q: P(1,0, 12). Consider h(x, y, z) = cos (ry) + e + In (az) at the point P llowing: it vector in the…

A:

Q: Evaluate the integral of vector function F(x,y) = x - y where the boundary curve is the triangle…

A: Given: Fx,y=xi-yj we need to find ∫F·dr, where r=xi+yj over the triangle formed by points…

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

A:

Q: mine the direction in which ƒ has maximum rate of increase from P. S(x, y, z) = x²y/z, P=(-1,2,16) e…

A: Given, fx,y,z=x2yz at Point P-1,2,16 The directional derivative is used to determine the direction…

Q: Find a vector parametrization for the line with the given description. Perpendicular to the…

A: Given points are (0,0,8). The equation of yz-plane is given by ⇒x=0 Therefore, the normal vector is…

Q: Find a vector parametrization r(t) for the line with the given description. Passes through P = (4,…

A:

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

A:

Q: Let f (x,y,z) = x2 + 2y - z and let P be the point (x , y , z) = (1 , 1 , 1). (i) Find the Minimum…

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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…

Q: A particle moves in a path defined by vector-valued fanction FH)=(t)i +(2t-3)j + ( 3t - 3t)K, where…

A: The tangential component, aT for r→(t) is calculated using the formula, aT=r'(t)·r''(t)r'(t) . The…