Suppose that a vector $$ with $$ elements is defined as follows: $=[1,2,...,].$ The magnitude of $$ is calculated by

squared each element of $,$ summing the results, and then taking the square root of the sum. That is to say:

magnitude $222$ of $=1+2++$

A unit vector is a vector whose magnitude is equal to $1.$ A unit vector can be created from any vector $$ by dividing each

element of $$ by the magnitude of $.$

Create a list named vector to represent the following vector: $[11,6,-8,4,-13,2].$ Then calculate the

magnitude of vector, storing the results in a variable named mag$\_$v$.$ You will need to use a loop to perform this

calculation. For the sake of efficient memory use, you should NOT create any additional lists to perform this calculation.

Recall that you can take the square root of a number by raising it to the power of $0\mathrm{.}5.$

Print the value of mag$\_$v rounded to $4$ decimal places. The value stored in the variable should not be rounded, only the

value displayed.

We will now create a unit vector from the vector we have created.

Use the values stored in vector and mag$\_$v to calculate a unit vector, storing the results in a vector named

unit$\_$vector. You will need to use a loop or a list comprehension to perform this task.

For the purposes of display, create another list named rounded$\_$unit$\_$vector. The elements of this list should be

calculated by rounding each of the elements of unit$\_$vector to $4$ decimal places. You can use a loop or a list

comprehension for this task.

Print the list rounded$\_$unit$\_$vector.

We will now calculate the magnitude of the second vector we created to confirm that it is$,$ in fact, a unit vector.

Calculate the magnitude of unit$\_$vector using the same technique you used to calculate the magnitude of vector.

Store the results in a variable named mag$\_$u$,$ and then print the value of this variable, without rounding it$.$

Note: Use unit$\_$vector instead of rounded$\_$unit$\_$vector to calculate mag$\_$u $($as instructed$).$ The list

rounded$\_$unit$\_$vector is used only for display purposes.