A man walking his dog walks around a perfectly square block. It starts at point A and walks clockwise around the block. Let r⃗ AB be the displacement vector from A to B, r⃗ BC the displacement vector from B to C, etc.
Answer 1
Vectors have a magnitude and a direction, such as “1 mile east”. They don’t have specific positions. So AB is the same vector as DC.
Each vector of AB, BC, CD and DA is in a different direction, so none of them are identical.
The negative of a vector has the same magnitude in the opposite direction, so -DA = AD.
To add vectors, think of them as arrows and remember that you can move them as long as you don’t rotate them. Try to match the end point of one with the start point of the other. The sum is a vector from the start point to the end point.
-DA = BC, then AB + (-DA) = AB + BC = AC
The answer to question 3 is all of the above.