Maths That Models Change
Vectors
13 min · 2 worked examplesStudent plan
Quantities with direction as well as size. Resolving, adding, and why a rope at an angle carries more tension than you expect.
After this lesson you can
- Split any vector into x and y components
- Add two vectors and find the resultant
- Say why resolving turns one hard problem into two easy ones
Size and direction
Some quantities need only a number: mass, temperature, energy. These are scalars. Others make no sense without a direction: force, velocity, acceleration. These are vectors.
A vector is usually written as components, how much of it points along x and how much along y. A force of 10 N at 30° above horizontal has a horizontal component of 10 cos 30° = 8.66 N and a vertical component of 10 sin 30° = 5 N.
That splitting is called resolving, and it is the single most useful operation in mechanics: once everything is in components you can treat the x and y directions as two entirely separate, ordinary problems.
In the full lesson
- Size and direction
- Adding vectors
- Why the angle matters
This lesson comes with the Student plan. The first module of Maths for Engineers is free.