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Vectors: magnitude, direction and products

Add, subtract and scale vectors · Diagrams · Complete reading

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Triangle law of addition

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Place b’s tail at a’s head. The directed diagonal a+b joins the initial tail to the final head, matching the page 3 source triangle.
Place b’s tail at a’s head. The directed diagonal a+b joins the initial tail to the final head, matching the page 3 source triangle.
Place b’s tail at a’s head. The directed diagonal a+b joins the initial tail to the final head, matching the page 3 source triangle.
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Commutative and associative addition paths

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Top: routes a then b and b then a around a parallelogram have the same resultant. Bottom: a then b then c has intermediate diagonals a+b and b+c; both groupings give the same final displacement.
Top: routes a then b and b then a around a parallelogram have the same resultant. Bottom: a then b then c has intermediate diagonals a+b and b+c; both groupings give the same final displacement.
Top: routes a then b and b then a around a parallelogram have the same resultant. Bottom: a then b then c has intermediate diagonals a+b and b+c; both groupings give the same final displacement.
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Subtraction and signed scalar multiplication

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The source subtraction reverses b and adds −b to a, giving a−b. Positive scalar multiplication keeps direction, negative scaling reverses it; zero scaling gives zero. Length illustrations are schematic.
The source subtraction reverses b and adds −b to a, giving a−b. Positive scalar multiplication keeps direction, negative scaling reverses it; zero scaling gives zero. Length illustrations are schematic.
The source subtraction reverses b and adds −b to a, giving a−b. Positive scalar multiplication keeps direction, negative scaling reverses it; zero scaling gives zero. Length illustrations are schematic.
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