Q: What is the product of two vector quantities?

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Charge is not a vector.

Because there are two different ways of computing the product of two vectors, one of which yields a scalar quantity while the other yields a vector quantity.This isn't a "sometimes" thing: the dot product of two vectors is always scalar, while the cross product of two vectors is always a vector.

It is the cross product of two vectors. The cross product of two vectors is always a pseudo-vector. This is related to the fact that A x B is not the same as B x A: in the case of the cross product, A x B = - (B x A).

The product of two vectors can be done in two different ways. The result of one way is another vector. The result of the other way is a scalar ... that's why that method is called the "scalar product". The way it's done is (magnitude of one vector) times (magnitude of the other vector) times (cosine of the angle between them).

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No, a scalar quantity cannot be the product of two vector quantities. Scalar quantities have only magnitude, while vector quantities have both magnitude and direction. When two vectors are multiplied, the result is a vector, not a scalar.

Vector quantities can be added and subtracted using vector addition, but they cannot be divided like scalar quantities. However, vectors can be multiplied in two ways: by scalar multiplication, where a scalar quantity is multiplied by the vector to change its magnitude, or by vector multiplication, which includes dot product and cross product operations that result in a scalar or vector output.

To determine a vector quantity, you need both magnitude (size or length of the vector) and direction. These two quantities are essential for describing a vector completely in a given reference frame.

The resultant of two vector quantities is a single vector that represents the combined effect of the individual vectors. It is found by adding the two vectors together using vector addition, taking into account both the magnitude and direction of each vector.

Charge is not a vector.

scalar, produced by the scalar product of two vector quantities ... Force · Distance

Scalar quantities - quantities that only include magnitude Vector quantities - quantities with both magnitude and direction

Two vector quantities can be combined into a scalar quantity because a vector lives in a vector space, which requires the existence of an operation called the dot product (also commonly known as the scalar product or inner product). The exact form of this operation depends on the type of vector space, and of course one can define other operations which map two vectors into a scalar. A commonly used definition is as follows: Imagine vector one contains these values (x1, x2, x3, x4) and vector two contains these values (y1, y2, y3, y4), the dot product would turn this into: x1*y1 + x2*y2 + x3*y3 + x4*y4 The dot product gives a measure of the angle between two vectors and is often used as such in for example mechanics.

The cross product is a vector. It results in a new vector that is perpendicular to the two original vectors being multiplied.

Two examples of vector quantities are velocity, which includes both speed and direction, and force, which consists of magnitude and direction.

Scalar product (or dot product) is the product of the magnitudes of two vectors and the cosine of the angle between them. It results in a scalar quantity. Vector product (or cross product) is the product of the magnitudes of two vectors and the sine of the angle between them, which results in a vector perpendicular to the plane containing the two original vectors.

Mainly because they aren't scalar quantities. A vector in the plane has two components, an x-component and a y-component. If you have the x and y components for each vector, you can add them separately. This is very similar to the addition of scalar quantities; what you can't add directly, of course, is their lengths. Similarly, a vector in space has three components; you can add each of the components separately.