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Vectors are written numerically in two equivalent ways: column vectors and i–j (component) form. Working in components turns vector addition into simple arithmetic on the numbers.
What you'll be able to do
A column vector stacks the horizontal and vertical components. The same vector in – form uses unit vectors (one unit right) and (one unit up).
In component form, add (or subtract) the matching components separately. No diagrams needed.
To multiply by a scalar, multiply component.
Tip — Keep i with i and j with j — never mix the two components.
Formula recap
Common mistakes to avoid
Key takeaways
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