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Definition
Definition
Algebraically, the dot product of 2 vectors a and b is defined as such:
Algebraically, the dot product of 2 vectors a and b is defined as such:
a • b = |a| |b| cos θ
where θ is the angle formed between the 2 vectors (placed tail to tail).
where θ is the angle formed between the 2 vectors (placed tail to tail).
Geometrically, the dot product gives a projection of one vector on the second vector.
Geometrically, the dot product gives a projection of one vector on the second vector.
Note that the dot product results in a scalar quantity.
Note that the dot product results in a scalar quantity.
Real World Examples
Real World Examples
A classic Physics example would be work done, the product of force and the distance moved in the direction of the force. If force and distance are not in the same direction, we need to project the displacement vector onto the force vector's direction and find the product of their magnitudes. Hence, work done = force • displacement
A classic Physics example would be work done, the product of force and the distance moved in the direction of the force. If force and distance are not in the same direction, we need to project the displacement vector onto the force vector's direction and find the product of their magnitudes. Hence, work done = force • displacement
A similar example is power = force • velocity
A similar example is power = force • velocity
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