Skalaarituotetta
Skalaarituotetta, also known as the dot product or scalar product, is a fundamental operation in linear algebra and vector calculus. It takes two vectors and returns a scalar value, which is the product of their magnitudes and the cosine of the angle between them. The dot product is denoted by a dot between the vectors, such as a · b.
The dot product of two vectors a and b in a Euclidean space is defined as:
a · b = |a||b|cos(θ)
where |a| and |b| are the magnitudes of vectors a and b, respectively, and θ is the angle
a · b = a1b1 + a2b2 + ... + anbn
where a1, a2, ..., an and b1, b2, ..., bn are the components of vectors a and b, respectively.
The dot product has several important properties, including commutativity (a · b = b · a), distributivity over vector
The dot product is widely used in various fields, such as physics, engineering, and computer graphics. In