Addition and subtraction of vectors 2d

Addition and Subtraction of 2D Vectors

A vector in 2D space is a quantity with both magnitude (length) and direction.
Vectors can be visually represented as straight arrows from one point to another.

Vector Addition

When you add vectors, you place them head to tail. The sum of two vectors forms a resultant vector, which starts from the tail of the first vector and ends at the head of the last vector.
In a Cartesian plane, vectors are added by adding the corresponding components. If a = (a1, a2) and b = (b1, b2), then a + b = (a1+ b1, a2 + b2).

Vector Subtraction

Subtracting a vector involves adding the opposite (or negative) of that vector. The negative of a vector is a vector of the same magnitude but in the opposite direction.
It’s helpful to remember that a - b is the same as a + (-b).
In terms of components, if a = (a1, a2) and b = (b1, b2), then a - b = (a1 - b1, a2 - b2).

Practical Applications

Addition and subtraction of vectors have numerous practical applications in physics, engineering, and computer graphics.
They can help to calculate movement in multiple dimensions, such as understanding the net force acting on an object, or calculating the direction and speed of a boat in a river with a current.

Remember, vectors are a fundamental concept in many areas of mathematics and physics. Understanding how to add and subtract them correctly will not only assist in solving mathematical problems, but also in visualising and solving real-world problems effectively.