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Basics of vectors for Edexcel A-level Maths

Basics of vectors

This page covers the following topics:

1. Column vectors
2. Cartesian coordinates
3. Unit vectors

Column notation (column vectors) and horizontal bracket notation (row vectors) can be used to express vectors. Horizontal bracket notation has no commas between the components, and should not be confused with coordinates.

Column vectors

To obtain the vector expression/equation, assume that the starting point of the vector is placed at the origins of an axes with labels i, j, k (you may consider them to be equivalent to x y and z axes). The vector equation is then given by how far along the vector goes with respect to these axes.

Cartesian coordinates

Unit vectors are vectors that have a magnitude of 1, no matter the direction. Often, they are used to denote axes. A unit vector can be obtained by dividing a given vector by its magnitude.

Unit vectors

1

Consider the vectors shown. What is the vector equation for vector a)?

v = โˆ’5i + 11j

Consider the vectors shown. What is the vector equation for vector a)?

2

Consider a unit cube. A vector which starts at the bottom left corner on the near face has it's other end at the top right corner in the far face. What is the vector equation for this vector?

v = i + j + k

Consider a unit cube. A vector which starts at the bottom left corner on the near face has it's other end at the top right corner in the far face. What is the vector equation for this vector?

3

Consider the 2D vector shown. What is the vector equation for this vector?

v = โˆ’3i โˆ’ 8j

Consider the 2D vector shown. What is the vector equation for this vector?

4

What is the equation for a unit vector going in the same direction as the vector shown?

โˆ’0.8i + 0.6j

What is the equation for a unit vector going in the same direction as the vector shown?

5

A vector is 5 units in x direction and negative 12 units in y direction. What would be the equation for a unit vector going in the same direction?

v = 5/13iย ฬ‚ โˆ’ 12/13jย ฬ‚

A vector is 5 units in x direction and negative 12 units in y direction. What would be the equation for a unit vector going in the same direction?

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