Vector Basics
Grade 6What is a vector?
A vector has both magnitude (size) and direction. A scalar has only magnitude. Speed is a scalar; velocity is a vector. Distance is a scalar; displacement is a vector.
Vectors are written as bold letters (a), underlined letters (a), or as column vectors where the top number is the horizontal component and the bottom is the vertical.
Column vectors
A column vector (3, −2) means: move 3 right and 2 down. A negative top means move left; a negative bottom means move down.
The magnitude (length) of a vector (x, y) is found using Pythagoras:
Worked example
Equal and negative vectors
Two vectors are equal if they have the same magnitude and direction — position doesn't matter. The vector −a is the same length as a but points in the opposite direction.
Try this one
Past paper - 2023
OABC is a parallelogram.
\(\overrightarrow{OA}=a\) and \(\overrightarrow{OC}=c\)
The point N lies on line AB such that AN: NB = 3: 5.
(a) Find the following vectors in terms of a and c. Give your answers in their simplest form.
(i) \(\overrightarrow{OB}\)=------------[1]
(ii) \(\overrightarrow{ON}=\)----------- [2]
(b) Line CN is extended to reach point P, such that \(\overrightarrow{CP}=\frac85\overrightarrow{CN}\)
Show, using vectors, that OAP is a straight line. [4]
