What is the vector representation of a displacement of 4 units right and 3 units up?

The vector representation of a displacement of 4 units right and 3 units up is (4, 3).

In mathematics, particularly in geometry and physics, a vector is a quantity that has both magnitude and direction. When we talk about displacement, we are referring to a change in position. In this case, moving 4 units to the right and 3 units up can be represented as a vector in a two-dimensional coordinate system.

The vector (4, 3) consists of two components: the first number (4) represents the horizontal displacement, and the second number (3) represents the vertical displacement. The horizontal component tells us how far to move along the x-axis, while the vertical component tells us how far to move along the y-axis.

To visualise this, imagine starting at the origin point (0, 0) on a graph. Moving 4 units to the right means you go from (0, 0) to (4, 0). Then, moving 3 units up means you go from (4, 0) to (4, 3). The final position (4, 3) is where you end up after the displacement.

Vectors are useful in many areas of maths and science because they can describe movements and forces in a clear and concise way. By using vectors, we can easily add, subtract, and analyse different displacements and forces, making complex problems simpler to solve.