Vector notation 2d
Vector notation 2d
Introduction to 2D Vectors
- A vector in two dimensions is defined by two components that are the magnitudes and directions in the x and y directions.
- A 2D vector can be represented in column form as [a b], where ‘a’ represents the x-component and ‘b’ represents the y-component of the vector.
- A vector can also be represented geometrically as an arrow possessing magnitude (length) and direction.
Vector Arithmetic
- Vector addition: To add two vectors, add the i (horizontal) components separately from the j (vertical) components. For instance, [a b] + [c d] equals [a+c b+d].
- Vector subtraction: To subtract one vector from another, subtract the i components and the j components separately. That is, [a b] - [c d] equals [a-c b-d].
- Scalar multiplication: To multiply a vector by a scalar (a number), multiply both components by the scalar. For example, k*[a b] equals [ka kb].
Zero, Unit and Parallel Vectors
- The zero vector [0 0] has no magnitude or direction.
- A unit vector is a vector with a magnitude of 1.
- Two vectors are parallel if they are scalar multiples of each other.
Position Vectors
- A position vector describes the position of a point relative to an origin.
- The position vector of a point P with coordinates (x,y) is written as [x y].
Displacement Vectors
- A displacement vector describes the shortest distance from one point to another.
- If the position vectors of points A and B are [a b] and [c d] respectively, then the displacement vector from A to B is [c-a d-b].
It’s necessary to understand these concepts and how to apply them in various situations for solving problems related to vectors in geometry.