Math History In 1827, the mathematician August Ferdinand Mbius publisheda book in which

Chapter 8, Problem 57

(choose chapter or problem)

Math History In 1827, the mathematician August Ferdinand Mbius publisheda book in which he introduced directed line segments (what we now call vectors).He showed how to perform scalar multiplication of vectors. For example, considera hiker who walks along a path given by the vector v. The path of another hiker whowalks twice as far in the same direction is given by the vector 2 v. a. Write the component form of the vectors v and 2 v.b. Find the magnitude of v and 2 v. How do they compare? c. Find the direction of v and 2 v. How do they compare? d. Given the component form of a vector, explain how to findthe components of the vector k v, where k is a constant. e. Use scalar multiplication with k = -1 to write the negationof a vector v in component form.