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kapoor_kapoor

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In summary, the conversation discusses the use of dot product and cross product in determining the result when multiplying two physical quantities or vectors. These mathematical operations have specific meanings in the context of physics and can provide information about the angle between vectors or the area of a parallelogram.

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kapoor_kapoor

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DEvens

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"Being multiplied" is likewise too vague to understand what is going on. For example, some quantities are a scalar times a scalar in some contexts. In other contexts they might be a scalar times a vector. Or a cross product. Or a dot product.

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mathman

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BobG

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kapoor_kapoor said:

A dot product will get you the angle between two vectors.

A cross product will get you a new vector that presumably represents some physical property (angular momentum, torque, etc). Geometrically, the magnitude of the cross product gives you the area of a parallelogram whose sides are defined by the two vectors you took the cross product of.

A vector is a mathematical quantity that has both magnitude and direction. It is often represented by an arrow pointing in the direction of the vector with a length proportional to its magnitude.

Vectors can be represented in several ways, including using Cartesian coordinates, polar coordinates, or using a column matrix. In physics, vectors are often represented using unit vectors in the x, y, and z directions.

A vector product, also known as a cross product, is a mathematical operation between two vectors that results in a third vector. It is used to find the direction and magnitude of a vector that is perpendicular to both of the original vectors.

The dot product of two vectors results in a scalar quantity, while the cross product results in a vector quantity. The dot product measures the projection of one vector onto another, while the cross product measures the perpendicular component of one vector to another.

Vector products have many applications in physics, engineering, and mathematics. They are used to calculate torque, magnetic fields, and forces in three-dimensional systems. In computer graphics, they are used to create realistic lighting and shading effects. In navigation, vector products are used to calculate the direction and speed of a moving object.

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