3. A hiker begins at the origin and walks in a straight line in the direction of the vector (1,1) for 2/2 kilometres, then in the direction of the vector (-1,1) for V2 kilometres, and then in a straight line back to the origin. (a) Plot the path of the hiker in the xy-plane, clearly marking the values of the coordinate where there is a change of direction. (b) Calculate the total distance travelled by the hiker. (c) By regarding the xy-plane as contained in R³, use an appropriate formula involving cross products to compute the area enclosed by the path of the hiker.
3. A hiker begins at the origin and walks in a straight line in the direction of the vector (1,1) for 2/2 kilometres, then in the direction of the vector (-1,1) for V2 kilometres, and then in a straight line back to the origin. (a) Plot the path of the hiker in the xy-plane, clearly marking the values of the coordinate where there is a change of direction. (b) Calculate the total distance travelled by the hiker. (c) By regarding the xy-plane as contained in R³, use an appropriate formula involving cross products to compute the area enclosed by the path of the hiker.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.3: Lines And Planes
Problem 18EQ
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