Equal and negative vectors

Equal Vectors

Vectors in maths represent a quantity that has both direction and magnitude.
Two vectors are considered to be equal if they have the same magnitude (length) and same direction.
In a diagram, two equal vectors will always be parallel and of the same length.

Negative Vectors

A Negative of a vector is simply a vector that has the same magnitude but in the opposite direction.
If you have a vector a, the negative of this vector is -a.
A good way to visualise this concept is to imagine the negative vector as pointing in the exact opposite direction of the original vector but with the same length.

Manipulating Vectors

You can perform basic mathematical operations on vectors, such as addition, subtraction and multiplication by a scalar.
Addition of vectors involves joining the vectors head-to-tail, and drawing a resultant vector from the tail of the first vector to the head of the last.
Subtraction of vectors can be visualised as the addition of a negative vector. If analysing vector a - b, it’s the same as a + -b.
Multiplication of a vector by a scalar changes only the magnitude (length) of the vector and may reverse its direction, depending on whether the scalar is positive or negative.

Understanding the concept of equal and negative vectors is important for manipulation of vectors and solving various vector-related problems in geometry. Remember to always consider both magnitude and direction when working with vectors.