Vectors are quantities that have both a magnitude and a direction.
Write the vector in a column, with the movement in the x-direction being the top number and the movement in they-direction being the bottom number.
A vector `((5),(7))` gives a displacement in the positive x direction, and 7 in the y direction.
Vectors are written in a number of ways.
The vector may be written to indicate the start and end points: `vec(AB)`. Direction is important: the vector is a displacement from A to B.
The vector can also be shown as a single letter: this is printed as a (bold a). When writing by hand, underline the letter: `ul(a)`.
Note that `vec(AB) = ul(a) = `a.
A column vector gives both magnitude and direction. The magnitude, or size, of a vector is written as |a| (called modular a). This means that the direction (when considering the size) is irrelevent and can be obtained using Pythagoras: for a vector `((x),(y))`, this is `sqrt(x^2 + y^2)`.
A vector that is equal to another vector has the same magnitude and direction, although they may not necessarily be at the same location.
Vector `vec(AB) = -vec(BA)`.
If vector `vec(AB)` = a and `vec(BA)` = b, then a = - b.
1. Vector a is defined as `((-3),(-4))`. Vector b is defined as `((4),(3))`. Does a = -b?
Answer: No; neither the x-displacement nor the y-displacement are equal and opposite.
2. Vector c is defined as `((7),(11))`. What is the magnitude of c?
Answer: 13.04 (to 2dp)
Use Pythagoras to determine the magnitude:
magnitude = `sqrt(7^2 + 11^2)`