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Show that the order of addition of three vectors does not
Chapter 3, Problem 8(choose chapter or problem)
Problem 8PE
Show that the order of addition of three vectors does not affect their sum. Show this property by choosing any three vectors A, B, and C, all having different lengths and directions. Find the sum A + B + C then find their sum when added in a different order and show the result is the same. (There are five other orders in which A, B, and C can be added; choose only one.)
Questions & Answers
QUESTION:
Problem 8PE
Show that the order of addition of three vectors does not affect their sum. Show this property by choosing any three vectors A, B, and C, all having different lengths and directions. Find the sum A + B + C then find their sum when added in a different order and show the result is the same. (There are five other orders in which A, B, and C can be added; choose only one.)
ANSWER:
Solution 8PE
We have to show that the order of addition of three vectors does not affect their sum and also show this property by choosing any three vectors A, B, and C all having different lengths and directions.
Let us illustrate this property by taking an example.
A student walks for 2 blocks North from his school before making a right hand turn and walks 4 blocks to the East. Finally, the student makes a left hand turn and walks a block to the North to reach his home.What is the magnitude of the overall displacement of the student.
The magnitude of the overall displacement of the student can be calculated by adding the vectors graphically using the head-to-tail method.
Represent each displacement vector graphically with an arrow, labeling the first A , the second B and the third C ,making the lengths proportional to the distance and the directions as specified relative to an east-west line.
A = 2 blocks North, B = 4 blocks East, C =1 block North