Consider the equilateral triangle with vertices A, B and C, and the following op
ID: 1836193 • Letter: C
Question
Consider the equilateral triangle with vertices A, B and C, and the following operations O; I: no rotation, or a 360-degree rotation. R1 = counterclockwise 120-degree rotation R2 = counterclockwise 240-degree rotation (All rotations are counterclockwise) Ra = reflection about the vertical midline passing through a: this axis is fixed. Rb = reflection about the midline passing through b: this axis is fixed. Rc = reflection about the midline passing through c: this axis is fixed. Fill out the table below for the result of two consecutive operations, O2O1, the first one on a labeled row and the second on a labeled column. Then find one single operation that goes from the original triangle above to O2O1. Record this result in the table. Some examples are given below. Q1: When does O2O1 = O1O2? Give two examples and two counterexamples. Q2: A mass M is placed on each vertex A, B, and C of the previous triangle, and a different mass mu is placed at the center of the triangle. What is the gravitational force on mu? Justify and explain fully your answer based on the symmetry of the system.Explanation / Answer
1)O2O1 = O1O2 WHEN EITHER O1 orO2 BELONGS TO ROTATION OPERATION
examples
R1R2 = R2R1
R1Ra = RaR1
counter examples
RaRb is not equal to RbRa
RbRc is not equal to RcRb