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Vector representation
Beginner
Arrows with length for magnitude and direction for orientation.
Draw a vector as an arrow: its length is proportional to magnitude and the arrowhead shows direction. Written as bold letters or with a bar. A vector can be moved without changing it as long as length and direction stay the same.
A force of 10 N at 30° above the x-axis is drawn as an arrow 10 units long inclined at 30°.
Angles must be measured from a stated reference axis; otherwise the same drawing can mean different things.
In more detail
A vector is drawn as an arrow whose length represents its magnitude and whose direction gives its direction. Vectors are written in bold or with an arrow above the symbol.
Real-world uses
- Maps use arrows to show wind or current direction and strength.
- Weather charts represent wind with arrows that show direction and speed.
- Force diagrams in engineering draw arrows for every push and pull, so the net effect on a structure can be seen at a glance.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
Does the position of a vector on the page matter?
No. A vector can be moved anywhere on the diagram as long as its length and direction stay the same.
How are vectors written in text?
Usually in bold or with an arrow, such as A or A with an arrow above it.
Does the length of an arrow have to be to scale?
Yes, in a diagram where the arrows represent quantities, their lengths should match the magnitudes on a chosen scale.
Related topics in Measurement & Math Tools
Order-of-magnitude estimates · Unit conversion · Scalars and vectors · Vector addition · Parallelogram law · Vector components