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.