A. Given force (F = F1 – F2), transform the force vector F to cylindrical coordinate system at point Р (10, -8, 6)? F1 = 25ax -17ay +12az F2 = 15ax +9ay +6az

Q: 2. Let f(x,y) = t Find the direction of a unit vector so that Daf is minimal at point (0, 1). %3D 3…

A: To find the direction of a unit vector u so that the directional derivative of f at point (0,1) in…

Q: O The vector fiel F CK,y,z) = (xy,y°z, 29 is given. Osing a svitable theorem, calculute finda on the…

A: Introduction: The surface integral of a vector field A over a closed surface is equal to the volume…

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: If the vector K ag+Lay+ Ma, shows the maximum increase rate and direction of the scalar Vat point…

A: If the vector Ka^x+La^y+Ma^z shows the maximum increase rate and direction of the scalar V at point…

Q: If three forces of (1N,-1N, 3N), (-3N,2N, -4N), and (3N,1N,-2N) act at on an object at a point in…

A: Angles made by equilibrium force with each x,y and z axis are given.

Q: Find the work done by a force q=5i+2j to move a body along the displacement from the points A(1,1,0)…

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Q: Find the work done by a force F = 4i + 9j (in N) in moving an object in a straight line from point…

A: Given:           F=4i+9j

Q: Given a cubic force in one dimension: F = a(x – a) (x – b) (x – c), find the coefficient k in the…

A: Substitute x=b+∈ F=αx-ax-bx-c  =αb+∈-ab+∈-bb+∈-c  =α∈∈+b-a∈+b-c  =α∈∈2b-a+b -c∈b-ab-c…

Q: Give the unit vector in spherical coordinates that extends from M(5,1,2) to N(2,4,5).

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Q: .3 Evaluate || F · dS, where F = and S is the helicoid with vector equation r(u, v) = 0<u < 1, 0 <…

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

Q: Q4/ For the force system shown in Fig. (1), find the forces F1 & F2 (Using Vectors) 30 45 F2 15

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Q: Find the work done by the force F (r, y) = yxi– (x – y) j over the straight line from (1, 1) to…

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Q: A force F = 2i -j- 3k is applied to an airplane with displacement vector D = i+2j + 2k. Express F as…

A: Let the force vector be F→=2i-j-3k and the displacement vector D→=i+2j+2k    F→=β1+β2   Here, β1 is…

Q: 1) Find the MAGNITUDE and DIRECTION of the RESULTANT of ALL the forces at point A +Y -120lb APPLIED…

A: The resultant of vectors at a point is defined as the net effect of the forces acting at the given…

Q: 2. A 6-mC (millicoulomb) positive charge is located in vacuum at P(3,-2,-4), and a 5-uC…

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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…

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Q: Find the work done by the force F in mving an object from P to Q. F = 2i – 4j; P(0, 0), Q(3, 6)

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Q: Find a vector tangent to the curve of intersection of the two cyclinders a? + y? = 8 and y? + 22 = 8…

A: Let fx,y,z=x2+y2 and gx,y,z=y2+z2 The gradient of the functions give the perpendiculars to the…

Q: The five forces and couple constitute a coplanar force system. Determine the resultant and locate it…

A: On solving the equation, To calculate ∈fx and ∈fy for forces, (support reaction is not to be…

Q: Determine the work done by the force F"(x,y,z)=(x²y,xy). to move a particle along the line segment…

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Q: Determine the work done in moving a particle from P to Q when the magnitude and direction of the…

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Q: 1.2. Given the following Force Vectors: FORCE VECTOR Flo 0 -50) F„[0 _0 -117] Fel-102 -12 77] F,[O 0…

A: 1. For F→A=-50k^, EA→=-9i^-5j^ M→=EA→×F→A   =i^j^k^-9-5000-50   =i^(250)-j^(450)+k^(0)M→=250i^-450j^…

Q: A rigid body is acted on by two forces, R =ai +bj - 3 at the point (1,2,-1) and F =i+aj+bkat the…

A: Given a rigid body is acted by two forces F1=ai^+bj^-3k^ at the point 1,2,-1 F2=i^+aj^+bk^ at the…

Q: Calculate the work done by the force F(x, y) = y?î+ xyj in moving a particle along the line which…

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Q: Q6/ A boxful has been moved a distance (2m) in a F = 5.2 i+ 3J horizontal direction due to effect of…

A: Work done by a force is equal to the product of Force applied in the direction of distance and…

Q: A rear wheel drive car is stuck in the snow between other parked cars as shown. In an attempt to…

A: (a) The equivalent force-couple system at the car center of mass G which will be given as - From a…

Q: (b) A force of F=5i+3j-2k is applied to an object, which moves it from A =i+j+kto В - 5i —j+2k.…

A: Follow step 2.

Q: - The vector component of the force (3i- j + 2k)N in the direction of the vector (-4j + 3k) is A…

A: The solution is given as

Q: di vergen a of the vector funchion v = xi+ 29j+ 32k, is Jhe 2

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Q: The cable AB prevents bar OA from rotating clockwise about the pivot O. If the cable tension is 670…

A: In the given figure let the length AB = x m. and angle(OAB) = theta. The angle (BOA) = 180° - 53° =…

Q: 1.A particle moves once counter clockwise about the triangle with vertices (0,0), (4,0) and (1,6),…

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Q: Find the work done by the force F = 9i – 6j in moving an object from the point (2, 4) to the point…

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Q: Three coplanar forces are given as follows: A = 4N eastward, B = 10 N at 125°, and C = 15 N at 220°.…

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Q: The volume of parallelepiped determined by the vectors u = 2i – k, v = 2j – 3k and .= w = i + j+k is…

A: We use the definition of the volume of a parallelopiped determined by the vectors a, b and c to find…

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: (2t, 1 – t, 4t) is a parametrization of the line passing through the point (0, 1,0) and also…

A: The statement : &lt;2t, 1-t, 4t&gt; is a parametrization of the line passing through the point (0,…

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: If a force F-2i -3j+k acts at the point (1,5,2), then the torque about z-axis is 13k 13 -13

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Q: Give the unit vector in spherical coordinates that extends from M(5,1,2) to N(2,4,6).

A:

Q: A force F = 2i + j - 3k is applied to a spacecraft with velocity vector v = 3i - j . Express F as a…

A: We have given the force F = 2i + j - 3k with velocity vector v = 3i – j.

Q: Let W be the union of the second and fourth quadrants in the xy-plane. That is, let W= Complete…

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Q: Part 1: Three forces lying on the xy-plane are applied on a rock stuck on the ground (situated at…

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Q: (b) Solve the electric flux through a paraboloid z = x² + y² – 16 that lies below plane %3D z = 0.…

A: As per our guidelines, we can only solve first question and rest can be reposted. The solution for…

Q: 2. Determine the resultant R of the two forces by a. Applying the parallelogram rule b. Summing…

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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: |A force F = 9i + 8j – 4k is applied to a spacecraft with velocity vector v = 2i – 7j. Express F as…

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Q: If c represents a constant force, find the work done if the point of application of c moves along…

A: The formula for work done is: W=F·s Where, F is the force and s is the displacement. If the initial…

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

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