16. a(1) = t i + e'j+ e¯'k, v(0) = k, r(0) = j + k

Q: (b) Amovingparticle starts at an initial positionr(0) = 1li + 2j +1k withinitial velocity v(0) = li…

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Q: Suppose a particle, whose initial position is (1, 0, 0), moves with velocity given by v(t) = (-1,…

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Q: a(t) = ti + e¹j+ek, v(0) = k, r(0) =j+ k

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Q: Find the velocity and position vectors of a particle that has acceleration a(t) = i+ 2 j, initial…

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Q: Q The position vector of a particle is given by s(t) = 3t² – 2t + 5.Find the time at which the…

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Q: (1) The position vector r of a missile at any time t is given by r = tį + (8t – t)j where į and j…

A: Solution by using formulaes :

Q: Consider a particle moving with a trajectory given by r(t)=x(t)i +y(t)j+z(t)k Discuss all changes in…

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Q: Consider the function f(x.y) = x(/y +x) and the point P (3,9). (a) Find the gradident vector of f at…

A: The function f(x,y)=xy+x and the point P=3,9. We have to answer the following...

Q: (b) The path of a moving body is defined by r(t) = costi+ sint j + (2 - sint)k. (i) Show that the…

A: The path of the moving body is given by rt=cos t i+sin t j+2-sintk. The given cylinder is x2+y2=1…

Q: Determine a unit vector in the direction in whichf(x,y) = 4x³ y² increases most rapidly at point…

A: Given that : - f(x,y)=4x3y2    at  P(-1,1) A function f(x,y) increases most rapidly at pointy P(a,b)…

Q: An object moves in space with acceleration a(t) = 12t²i+6tj+2k. When t = 0, the object is at (1, 0,…

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Q: An airplane took off from point (3, 0, 0) at an initial velocity, v(0)= 3j with an acceleration…

A: Let r(t) be a position vector of a particle at time t. Then the velocity vector  v(t)=ddtr(t) Also…

Q: 3. (a) Find an equation for the tangent line to the curve parameterized by 3(t) = (. e"-) at the…

A: Given data: s→(t)=t3+t+2t2+1, et2-1 point p→=<0,1> So, x=0, y=1⇒t3+t+2t2+1=0et2-1=1=e0…