Consider the vector-valued function r(t) = (sin 2t + cos 2t)i + (sin 2t – cos 2t)j. (a) Find the arc-length of the portion of the curve from t1 0 to tz = R/4. (b) Find the parametric equations of its tangent lines at t =0 and t2 ==/4. (c) If 0 is the angle formed by the two tangent lines above, find cos 0.

Q: Consider the following parametric curve r(t) =

A: Let rt be the parametric equation of the curve. To calculate the unit tangent vector, use the…

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Q: Find the parametric equations of the tangent line LT to the curve C:r (t) = 2 cos(t)i + sin(t)j +…

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Q: Consider the parametric equations for a curve in the xy-plane given by: x = t^3 - 3t y = t^2 - 2…

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Q: X = e2t y = 2cost+ 6sint parametrik denklemleri ile verilen eğrinin (1,2) noktasındaki teğet…

A: Consider the given parametric equations. x=e2ty=2cost+6sint     at point(1,2)

Q: Graph the curve with parametric equations  x = sin(t), y = 3 sin(2t), z = sin(3t). Find the total…

A: x=sint, y=3 sin2t, z=sin3t We have to find the total length of the curve.

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.