Table of Contents
What is Cross Product?
The cross product is a vector operator that takes two vectors as input and produces a third vector as output. The cross product is defined as the vector product of two vectors, and is denoted by the symbol . Cross product is perpendicular to both input vectors, and its magnitude is equal to the product of the magnitudes of the input vectors multiplied by the sine of the angle between them. Cross Product – Formula.
The Cross-multiplication Formula
The cross-multiplication formula is used to solve systems of linear equations. The formula is as follows:
$\left(\begin{array}{c}a\\b\\c\\d\\e\\f\\g\\h\end{array}\right)=\left(\begin{array}{c}x\\y\\z\\w\\x\\y\\z\\w\end{array}\right)$
In the formula, $a$, $b$, $c$, $d$, $e$, $f$, and $g$ are the coefficients of the first equation, and $h$ is the coefficient of the second equation. $x$, $y$, $z$, and $w$ are the variables in the equation.
Properties of Cross Product
The following are some of the most important properties of the cross product:
1. The cross product is perpendicular to both of the vectors that are involved in the product.
2. The magnitude of the cross product is the product of the magnitudes of the two vectors, and the direction of the cross product is determined by the right hand rule.
3. The cross product is a vector quantity.
4. The cross product is associative – that is, the order of the vectors that are involved in the product does not affect the result.
5. The cross product is commutative – that is, the order of the vectors that are involved in the product does not affect the result.
6. The cross product is distributive – that is, the product of a vector and a scalar is the same as the vector cross product of the vector and the scalar.
Calculating Cross Product
To calculate a cross product, first identify the two vectors that you want to multiply. Next, use the following formula:
(A x B) = A.B sinθ
In this equation, A is the first vector, B is the second vector, and θ is the angle between the two vectors.
Cross Product – Formula.
