To illustrate that the length of a smooth space curve does not depend on the parameterization used to compute it, calculate the length of one turn of the helix with the following parameterizations. a. r(t) = (cos 4t)i + (sin 4t)j + 4tk, 0 sts5 b. r(t) = cos sin j+ Osts 4x c. r(t) = (cos t)i - (sin t)j - tk, - 2xstso Note that the helix shown to the right is just one example of such a helix, and does not exactly correspond to the parametrizations in parts a, b, or c. a. L=O (Type an exact answer, using x as needed.)

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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.