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I got asked how the scalar product can be used to find the length of a vector? Could someone please explain
UltrafastPED said:Do you mean vector product, also called the dot product?
V°V = |V|^2.
Or do you mean the triple scalar product:
|A°BxC|= volume of the parallelepiped with three sides defined by A,B,C.If it is the triple scalar product you will need more information to obtain a vectors length - but the dot product provides it immediately.
FeDeX_LaTeX said:To my knowledge, the vector product and the dot product are never given the same meaning. The vector product yields a vector quantity; the dot product yields a scalar quantity.
The scalar product, also known as the dot product, is a mathematical operation used to find the projection of one vector onto another vector. It can also be used to find the length of a vector in a given direction.
The scalar product is calculated by multiplying the magnitudes of two vectors and the cosine of the angle between them. The formula is given as: A · B = |A| |B| cosθ, where A and B are the two vectors.
The scalar product is used in physics to find the work done by a force on an object, as well as the angle between the force and displacement vectors. It is also used to find the component of a force acting in a particular direction.
In geometry, the scalar product is used to find the angle between two vectors, as well as the length of a vector. It is also used to determine if two vectors are perpendicular or parallel to each other.
Yes, the scalar product can be negative if the angle between the two vectors is greater than 90 degrees. This indicates that the vectors are pointing in opposite directions, resulting in a negative value for the scalar product.