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Back to Vectors

Vectors and Coordinates

An arrow you can drag and a pair of numbers you can type are the same object. Move one and watch the other follow — and get the length for free from Pythagoras.

Step 1 of 22

Speed

This arrow starts at the origin and its tip sits at the point (3, 2). Those two numbers are the whole vector: v = (3, 2). An arrow and a list of numbers are two ways of writing the same thing.

v =

|v| = ?tail at (0, 0), tip at (3, 2)

\mathbf{v} = \begin{bmatrix} \textcolor{#4ade80}{3} \\ \textcolor{#f87171}{2} \end{bmatrix} = \textcolor{#4ade80}{3}\,\hat{\imath} + \textcolor{#f87171}{2}\,\hat{\jmath}

Green is how far across, red is how far up. Typing a component moves the tip; dragging the tip retypes the components.

Vectors and Coordinates

An arrow you can drag and a pair of numbers you can type are the same object. Move one and watch the other follow — and get the length for free from Pythagoras.

Step 1 of 22

Speed

This arrow starts at the origin and its tip sits at the point (3, 2). Those two numbers are the whole vector: v = (3, 2). An arrow and a list of numbers are two ways of writing the same thing.

v =

|v| = ?tail at (0, 0), tip at (3, 2)

\mathbf{v} = \begin{bmatrix} \textcolor{#4ade80}{3} \\ \textcolor{#f87171}{2} \end{bmatrix} = \textcolor{#4ade80}{3}\,\hat{\imath} + \textcolor{#f87171}{2}\,\hat{\jmath}

Green is how far across, red is how far up. Typing a component moves the tip; dragging the tip retypes the components.

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Vectors and Coordinates

See also

Vectors and Coordinates

See also