The result of adding two vectors of equal magnitudes in opposite directions is a zero vector.
Vectors are mathematical or physical quantities that have both magnitude (size or strength) and direction. When we add vectors, we combine their effects, taking both their magnitudes and directions into account.
The Effect of Opposite Directions and Equal Magnitudes
When two vectors have the same magnitude but point in exactly opposite directions, their effects counteract each other completely. Think of two equal forces pushing on an object from opposite sides – if the forces are equal, the object doesn't move because the forces cancel out.
As stated in the provided reference: "Given the two vectors are of equal magnitudes but they are in opposite directions. Therefore they will cancel each other. And the resultant vector will be a zero vector. The sum is a zero vector." This means the net effect of adding such vectors is zero.
What is a Zero Vector?
A zero vector, also known as a null vector, is a special type of vector.
- It has a magnitude of zero.
- It has no specific direction, as a point (zero magnitude) doesn't point anywhere.
It represents no displacement, no force, no velocity, etc.
Practical Example
Consider the displacement of an object:
- Suppose you walk 10 meters East (Vector A).
- Then, you walk 10 meters West (Vector B).
Vector A has a magnitude of 10 m and points East. Vector B has a magnitude of 10 m and points West (the opposite direction). When you add Vector A and Vector B to find your total displacement:
- You return to your starting point.
- Your total change in position is zero.
The resultant vector (the sum of Vector A and Vector B) is a zero vector.
Summary of Result
Adding two vectors with equal magnitude but opposite directions results in a zero vector.
| Vector 1 | Vector 2 | Direction Relation | Magnitude Relation | Resultant Vector |
|---|---|---|---|---|
| Magnitude X, Direction A | Magnitude X, Direction Opposite of A | Opposite | Equal | Zero Vector |
This principle is fundamental in physics and engineering, explaining why opposing forces or movements of equal strength lead to no net change or zero resultant effect.
