If the position vector r(t)=e9t i +9sqrt(2)t j + e-9t k, compute the normal component of the acceleration (aN).

Q: The position vector r describes the path of an object moving in space. Find the velocity v(t), speed…

A: Velocity,v(t) = dr/dt Acceleration, a = dv/dt

Q: If r(t) is the position vector of a particle in the plane at time t, find the indicated vector. Find…

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Q: Consider R = xi +yj+zk and r = a constant vector A = a1 +a2 í + az k: What is (A. V)R in terms of A?…

A: R→=xi→+yj→+zk→ and r=R→, a constant vector A→=a1i→+a2j→+a3k→

Q: Given an acceleration vector, initial velocity (uo.vo), and initial position (xo.Yo). find the…

A: v(t)=∫at dt =∫1,4 dt=t,4t+Cwhere C is the constant vector ie, C=2,5 which is obtained from the…

Q: Given an acceleration vector, initial velocity (uo.Vo. wo), and initial position (xo,YoZo), find the…

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Q: Let the velocity vector be v(t) = (6 cos(3t), 8 exp(2t), 3t2). Compute the acceleration vector a(t).

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Q: Given an acceleration vector, initial velocity (up.vo), and initial position (Xg.Yo), find the…

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Q: Find a equation vector and the equation of the tangent line at the point P0 where t=0.2 on the graph…

A: The tangent is the line that just touches the curve at the point. The equation for the tangent line…

Q: If r(t) = −6ti + 4t²j – 8tk, compute the tangential and normal components of the acceleration…

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Q: Assume that an object moves on a trajectory according to the equations x(t)=t+cost, y(t)=t−sint.…

A: An object moves on a trajectory according to the equations  Differentiating  with respect to t, we…

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.