How to denote Vectors

There are a number of ways to denote vectors.

Using a single letter to denote vectors

We can use a letter e.g. a, b, etc. to denote a vector. This letter used should be a lower case letter. When typed, we bold these letters to indicate that they are vectors. However, when we write them out, we write a curly line beneath the letter to show that they are vectors.

For your exam, you will be writing the vectors, hence, you are required to put the curly line beneath the letters when representing vectors.

When we denote vectors, we use bold letters to represent vectors. When writing them out, we put a curly line beneath the letter to represent vectors.

Representing Vectors by the start and end point

We can represent vectors by the start and end point. Upper case letters are used to represent the start and end point, and we put an arrow above the 2 letters.

For instance, if we are interested in the vector from point A to point B, then it is written as:

Representing Vectors in x, y- direction (for 2-dimensional vectors)

There are 2 ways to represent vectors in 2-dimension using x, y- coordinate system.

One way is by using the unit vectors i and j. One unit of i represents 1 unit in the x-direction. One unit of j represents 1 unit in the y direction.

Hence, if a vector is displaced a units in the x-direction and b units in the y- direction, we can write it as ai + bj.

Alternatively, we can also express vectors in x,y- coordinate system in this manner:

Vector AB in x,y- coordinate system. To represent such vectors, we look at the displacement in the x- drection and the displacement in the y-direction.

Representing Vectors in x, y, z- directions (for 3-dimensional vectors)

There are 2 ways to represent vectors in 3-dimension using x, y, z- coordinate system.

One way is by using the unit vectors i, j and k. One unit of i represents 1 unit in the x-direction. One unit of j represents 1 unit in the y direction. One unit of k represents 1 unit in the z direction.

If a vector is displaced a units in the x-direction, b units in the y- direction, and c units in the z-direction, we can write it as ai + bj + ck.

We can also express ai + bj + ck this way:

Notes on H2 Math Vectors

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All the notes for H2 A Level Math

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