2 - dimensional vectors are mathematical objects that have both magnitude and direction. They are commonly used in physics and engineering to represent physical quantities such as velocity or force.
2 - dimensional vectors are typically represented as an ordered pair of numbers, with the first number representing the magnitude and the second number representing the direction. They can also be represented graphically as arrows on a coordinate plane.
To add or subtract 2 - dimensional vectors, you simply add or subtract the corresponding components of the vectors. For example, to add (3, 2) and (1, 5), you would add 3 + 1 = 4 for the first component, and 2 + 5 = 7 for the second component, resulting in a new vector of (4, 7).
The magnitude of a 2 - dimensional vector is the length of the vector, calculated using the Pythagorean theorem. It is represented by the absolute value of the square root of the sum of the squares of the vector's components. For example, the magnitude of (3, 4) would be √(3^2 + 4^2) = √25 = 5.
There are two types of multiplication for 2 - dimensional vectors: scalar multiplication and dot product. Scalar multiplication involves multiplying a vector by a scalar (a single number), resulting in a new vector with the same direction but a different magnitude. Dot product involves multiplying the corresponding components of two vectors and then adding them together, resulting in a single number representing the magnitude of the projection of one vector onto the other.