Frod the dietonal derivatie of the fnetion fxkens an the vector direction Making an angle of +60°wth the posttre X-axPst at point (0,F).

Q: Determine if the vector feld F(=,3=-2) = (24=?y"=", 482"y7=,42'y4) is conservative on R". Select the…

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

A: position vector given <sin2t , cos5t> speed = ?    at   t =2

Q: Find the ualt noima vector fol for Rhe Lvector valuhed P(4)=t t? and sketch the durve the vector…

A: To Find:

Q: For vectors i : onto v. and w = calculate the scalar projection of w %3D comp;w (Give an answer…

A: scalar projection of w on v is =v.w|v||w|compvw¯=…

Q: Evaluate | F. dS , where F = and S is the helicoid with vector equation r(u, v) = 0 < u < 4, 0 < v…

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Q: Hhewet Fint projection and Vector projiction ofBonto Afar: A-B, angte between A andBslength_of - -A=…

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Q: Evaluate /| F - d5 , where F = and S is the helicoid with vector equation r(u, v) 0 < u < 4, 0 < v…

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Q: Qe A Find the Vector 5 unit length in the direction of vector perpendicular to the iplane which…

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Q: Suppose the tenuper a ture at a point (x,y,2) is represen ted by the following: T(2,y,2) = 10e2x* -…

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Q: A force is specified by the vector F 80i - 40j + 60k lb. Calculate the angles made by F with the x-,…

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Q: Express in cylindrical components: (a) the vector from C(3, 2, -7) to D(-1, -4, 2); (b) a unit…

A:

Q: Evaluate F.dS, where F = and S is the helicoid with vector equation r(u, v) = 0 < u < 3, 0 < v < T…

A: Given that, F¯=y,-x,z5 and ru,v=u cos v, u sin v, v where 0≤u≤3 and 0≤v≤π. Find ru×rv as follows.…

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: What is the i-component of unit vector of the vector u ? Give your answer correct to two decimal…

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Q: Consider an object moving according to the function from position r(t) = acoswt i + asenwt j. To…

A: As per the question we have to find the tangential and normal vector components of the path defined…

Q: nit vector u in the direction opposite of V v = 4 i – 5j +3k.

A: The question is taken from the vector in which we have to find the uniye vector opposite to the…

Q: Howed Find efuation fer fendicular to the vector from origin to A. of the plane through…

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Q: Evaluate F· dS , where F = and S is the helicoid with vector equation r(u, v) upward orientation.…

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Q: which vector is NOT orthogonal to (cos θ, sin θ, 1)? a) (-sin θ, cos θ, 0) b) (-cos θ, -sin θ, 1)…

A: To find which vector is not orthogonal to (cosθ,sinθ,1)

Q: A particle moves on a fixed surface in F.(0), which is defined by z = 2xy. During the motion, the x…

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Q: Evaluate || F . d5, where F = and S is the helicoid with vector equation r(u, v) = Is 0 < u < 4, 0…

A: The solution are next step

Q: Evaluate F - dS, where F = and S is the helicoid with vector equation r(и, о) - = 0 < u < 2, 0 < v…

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Q: Find the binormal vector, curvature and radius of curvature for the vector function r=3 cos 3ti +…

A: The radius of curvature is the reciprocal of the curvature which is reciprocal of Kapha is the…

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: Find a unit vector u in the direction of v. Verify that |u| = 1. %3D v = (1, -7) U =

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Q: Find a unit vector u in the direction of v. Verify that ||u|| 1. %3D v= (12, -5) V = u =

A: Given: v=12,-5 =12i^-5j^ Unit vector in direction of vector a→ is defined as a→a→, where a→ is the…

Q: Consider the line Siven by the Purumetric euvaton X=2434 Y=-1-+,2+ Q Find dinection vector of this…

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Q: 58. Refer to Exercise 56. a. Find the component vector of F perpendicular to the ramp. Round values…

A: The component vector of F perpendicular to the ramp is  F = F1 + F 2 F2 = F - F1  F2 = -200j- (46.9i…

Q: Evaluate /| F. d5 , where F = and S is the helicoid with - vector equation r(u, v) = 0 < u < 1, 0…

A: To evaluate the below vector surface integral. ∫∫SF⋅dS

Q: 7. For vectors a and b in R? prove Lagrange's identity: ||a x b|? = ||a|| ||b||? – (a · b)?

A: for vectors a and b in ℝ2 prove -lagrange's identity a×b2=a2b2-a·b2

Q: Express in cylindrical components: (a) the vector from C(3, 2, –7) to D(-1, –4,2); (b) a unit vector…

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Q: A friengle Central vector is formed hy vectous, the i tjtk, ond one its Surroundiny Side is zi-3 j…

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Q: LOCATE THtE NUMBERS 2 and z, vectorially (show your illustraton), APD uSE THっE vもCtDes TD 千ND A) 2,+…

A: Solution

Q: Find all unit vectors parallel to the JZ plane and perpendicular to the vector V = 5i -j + 2K %3D

A: A vector is parallel to yz-plane and perpendicular to the vector v, we have to find the unit…

Q: Qy: In VĘ CR) find all vectors which are orthegonal to u=(1,-2, 3) uut corath

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Q: Dot product from the definition Compute u ⋅ v if u is a unit vector, | v | = 2, and the angle…

A: To Determine:  Dot product from the definition Compute u ⋅ v  Given:  u is a unit vector, | v | = 2,…

Q: tind a non-zero vector perpendıcular to the vectar u. Find the length of the vector R-

A: Consider two vector u→=ai→+bj→ and v→=ci→+dj→ if the two vector is perpendicular then the angle…

Q: A force F of 6 units acts through the point P = (2, 3, 1) in the direction of the vector (4, 1, 2).…

A: the moment formula M= r×F here r = vector PQ r =  OQ→-OP→ = (-1,-1,0) And the F vector is 6 times…

Q: Determine the moment of the force F = -40i + 30j + 20k kN about axis OA using vector method.

A: To determine: the moment of the force F → = - 40 i → + 30 j → + 20 k →  N about axis OA using vector…

Q: Two individuals are attempting to relocate a sofa by applying forces in the indicated directions. If…

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Q: . Let 7 - " be the separation vector from a fixed point (a', y', z') to the point (x, y, z). Show…

A: we have,  fixed point x',y',z'=r' and point x,y,z =r  r→-r→'=x-x'i^+y-y'j^+z-z'k^ a…

Q: Q when analyzing the vector Å-zi-j+3K To theSum Parallet to the ve ctor 3=i+2j+zk etwo vectors Lirst…

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Q: (a) f(r, y) = xª – x²y+y² +6 at P(-1,1) (b) f(r, y) = 2 sin(2x – 3y) at P(0, 7)

A: Please see the explanation below

Q: Evaluate F. dS, where F = and S is the helicoid with vector equation r(u, v) , 0 < u < 3, 0 < v <…

A: Given the vector field F→=y,-x,z2 and the surface S is parametrized as ru,v=ucosv,usinv,v,…

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: Evaluate F. dS, where F = and S is the helicoid with vector equation r(и, v) with upward…

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Q: A force of 40lbs acts on a body at an angle of 30°. Express the force vector in component form and…

A: Vector

Q: Ex. het be the vector Share sf 3*3 Symmetric motrices R. Show that dinW=6

A: Dimension of n × n symmetric matrix is n(n+1)/2

Q: Evaluate F. dS, where F = and S is the helicoid with vector equation r(u, v) = 0< u < 2, 0 < v <…

A: