t2 3. r = (2 1n(1+t))i+ (t²)j +tk t= 1 T 4. r = (e-t)i+ (2 cos 3t)j + (2 sin 3t)k t= Find the particles veloc ity and acceleration vectors. Then find the particles speed and direction Example of motion at the given value of t. e 11:10 vA

Q: 3. r = (2 ln(1+t))i + (t²)j + tk t=1 4. r (e-t)i+ (2 cos 3t)j+ (2 sin 3t)k t Find the particles…

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Q: The acceleration of a moving object is given by ā(t) = cos (2t)i+ 4t³j+ 6sin (3t)k. The initial…

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Q: Q2) consider a particle moving in a curve defined by F(t) =sin 21, cos 21, 1. Find a. The velocity…

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Q: 5) The position vector of a particle is given by s(t) = 3t² – 3t + 4.Find %3D the time at which the…

A: From the given problem:   st=3t2-3t+4   As we know that the expression of the instantaneous velocity…

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Q: 1. Suppose that r(t) = (3 cos(3t) · t, 3 sin(3t), 5t). a. Determine the velocity, the acceleration…

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A: The position vector of particle P of mass 2 kg at time t seconds is given by r=1-cos2ti+1+sin2tj.

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Q: 3. Use the given acceleration function to find the velocity and position functions, and then find…

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Q: 5) The position vector of a particle is given by s(t) = 3t2 - 5t + 5.Find the time at which the…

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Q: 10:13 AM Fri Oct 30 L 37% T 4) Let slt) = - 36+ 66+ 3, t z0, give the position of an obyect moving…

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Q: t3 Find the vector equation of the tangent line to 7(t) = 2 (e1-t) In t i+ tan-1 tj+ k at cos(t t)…

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Q: 5) The position vector of a particle is given by s(t) = 2t2 – 5t + 4.Find the time at which the…

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Q: Answer the Following: a) If A = 31 + 2j , B = 5j+ k , find A. B, A x B. b) 7(t) = (t + 1)i + (t² –…

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Q: 4. r = (e-)i+ (2 cos 3t)j+ (2 sin 3t)k t= Find the particles veloc ity and acceleration vectors.…

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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.