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3D vectors

3D vectors

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3D vectors are added by adding their corresponding coordinates or by connecting them β€œhead to toe”.

Adding 3D vectors

To subtract 3D vectors, reverse the direction of the vector that is subtracted or subtract corresponding coordinates.

Subtracting 3D vectors

Two vectors can be multiplied by using a dot product, which can be obtained by multiplying corresponding coordinates and adding the results up. Alternatively, cosine value of an angle between the vectors may be used.

Multiplying 3D vectors

2D Pythagoras’ theorem can be modified to obtain the magnitude of a 3D vector. The final equation is M = √(aΒ² + bΒ² + cΒ²).

Magnitude of 3D vectors

Vectors are perpendicular if cosΘ = 0.

Proof with 3D vectors

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