Prove the triple product identity Ax(B×C)= B(A·C)-C(A·B).

Q: Given a space curve C with position vector 3 cos 2t i + 3 sin 2t j + (8t – 4)k r Find a unit tangent…

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Q: Vectors A and B are given by: A = 40.62i+ 85.71j B = 81.48i + 13.19j Find the scalar product AB.

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Q: L,, Ly] = L,Ly – LyL = ihL, %3D %3D

A: We know, Lx^=y^pz^-z^py^Ly^=z^px^-x^pz^Lz^=x^py^-y^px^

Q: Consider two vectors Å = -5î – 3j + 2k and B = -8j - 2k, find the angle between vectors Å and B.

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Q: A A T4!= "T7-"T7= "77

A: The angular momentum of x  and z component is defined as…

Q: Find the polar coordinates corresponding to a point located at (-5.00, 12.00) in Cartesian…

A: The relation between Cartesian coordinates (x, y) and polar coordinates (r, θ) be defined as,

Q: jxi=-k_This The convention is to choose the direction of +z so that ?Xj=kv which automatically means…

A: Given values: Force, F→=(7i^+9i^) N Displacement, r→=(0.8i^+1.2i^) m Torque, 𝞃→ = r→×F→

Q: Express the vector field D = (x²+y²)⁻¹ (X2x + Y2y) in cylindrical components and cylindrical…

A: Given Express the vector field D = x2+y2-1  xax+yay in cylindrical components and cylindrical…

Q: the eigenvalues of the following matrix: /2 2 0 220 0 0 A) 0, 1,4 B) 1.2.2 C) 5,0,0 D) 5, 5,0 E) 0,…

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Q: Vector A has a magnitude of 4 m and lies in the xy plane directed at 45 degrees counterclockwise…

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Q: Express the vector directed from point A(3,2,-7) to point B(-1,-4,2) in cylindrical coordinates.

A: given, point A(3,2,-7) , B(-1,-4,2)cylindrical coordinate is (ρ,ϕ,z)ρ=x2+y2 ,ϕ=tan-1yx, z=zfor point…

Q: Find a vector equation for the line through the point (-4, 8, 2) perpendicular to the plane –7x – 7y…

A: Given  Equation of plane is. -7x-7y+7z = 16 Point on line is. (-4,8,2)

Q: Two vectors a→ and b→ have the components, in meters, ax = 5.04 , ay = 2.15 , bx = 1.40 , by = 5.72…

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Rigid Body

A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.

Rigid Body Dynamics

Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).