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In this section, we develop an operation called the cross product, which allows us to find a vector orthogonal to two given vectors. Calculating torque is an important application of cross products, and we examine torque in more detail later in the section.
The cross product (written $\vec{a} \times \vec{b}$) has to measure a half-dozen “cross interactions”. The calculation looks complex but the concept is simple: accumulate 6 individual differences for the total difference.
Given two linearly independent vectors a and b, the cross product, a × b (read "a cross b"), is a vector that is perpendicular to both a and b, [1] and thus normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming.
A vector has magnitude (how long it is) and direction: Two vectors can be multiplied using the "Cross Product" (also see Dot Product) The Cross Product a × b of two vectors is another vector that is at right angles to both: And it all happens in 3 dimensions!
The cross product of two vectors, say A × B, is equal to another vector at right angles to both, and it happens in the three dimensions. Cross Product Formula. If θ is the angle between the given two vectors A and B, then the formula for the cross product of vectors is given by: A × B =|A| |B| sin θOr,
A cross product is denoted by the multiplication sign (x) between two vectors. It is a binary vector operation, defined in a three-dimensional system. The cross product of two vectors is the third vector that is perpendicular to the two original vectors.
The cross product is defined only for three-dimensional vectors. If $\vc{a}$ and $\vc{b}$ are two three-dimensional vectors, then their cross product, written as $\vc{a} \times \vc{b}$ and pronounced “a cross b,” is another three-dimensional vector.