For AI agents: use /llms.txt for the Nakafa content index.
Vector subtraction is one of the basic operations in vector mathematics. Unlike vector addition that combines two vectors, vector subtraction produces the difference between two vectors. When we subtract vector from vector , the result is a vector that, when added to , will produce .
Mathematically, vector subtraction is defined as:
This means that subtracting vector from vector is equivalent to adding vector with the negative of vector .
Geometrically, vector subtraction can be depicted by:
The resulting vector, , can also be obtained by drawing a line from the endpoint of vector to the endpoint of vector when both vectors are drawn from the same origin point.
Vector subtraction can be performed by subtracting corresponding components. Suppose we have two vectors:
Then vector subtraction can be calculated as:
For two-dimensional vectors, the equation becomes:
Suppose there are two vectors:
Vector subtraction is:
While vector subtraction is:
Note that in general. In fact, .
Vector subtraction has many applications in real life:
Calculating Displacement: If is the final position and is the initial position, then is the displacement vector.
Calculating Distance: In games like Angry Birds, vector subtraction is used to calculate the distance and direction between the bird and the target.
Physics: Vector subtraction is used to calculate the resultant force in systems with multiple forces.
Vector subtraction can also be used to find the resultant vector. A resultant vector is a vector that represents the combined effect of two or more vectors.
Suppose an object moves from initial position to final position . The displacement vector of the object is:
This resultant vector shows the direction and distance of the object's displacement.
Vector subtraction has several important properties:
A monkey is at position and wants to get a banana located at position . Determine the displacement vector of the monkey to reach the banana.
Solution:
Monkey's position: Banana's position:
Displacement vector of the monkey to the banana:
Therefore, the monkey needs to move in the negative -axis direction and in the negative -axis direction to reach the banana.
The magnitude of the displacement vector can be calculated using the Pythagorean theorem:
