Cross product formula

About Cross product formula

The cross product is a binary operation on two vectors in three-dimensional space. It produces a new vector that is perpendicular to both. The right-hand rule is used to calculate the cross-product of two vectors.

According to the right-hand rule, the resultant of any two vectors is perpendicular to the other two vectors. We may also determine the magnitude of the resulting vector by using cross-product.

Definition of Cross Product Formula

Vector product/cross product of vectors A→ and B→ is denoted by A→ × B→ and its resultant vector is perpendicular to the vectors A→ and B→.

Cross Product Formula

Formula is given as :

A→ × B→= ABSinθ &ncirc;, where θ is the angle between the given vectors,

Here, &ncirc; denotes unit vector

Cross Product of Two Vectors

cross product of two vectors is indicated as,X→ × Y→ = |X→|.|Y→| sinθ

Let us take any two vectors X→ = xi→ + yj→ + zk→and y→ = a i→ + bj→ +c k→

Matrix form, also known as determinant form, can be used to define the cross product of these two vectors.

X→ × Y→ = i→(yc -zb) - j→(xc - za) + k→(xb - ya)

Cross Product Rules

Anti-Commutative Property: Cross product is anti-commutative property i.e., it means A→ × B→ = -B→ × A→

let A→ = a 1i→ + a 2j→ + a 3k→ and B→ = b1i→ + b2j→ + b 3k→ ,

Cross product formula1

= -A→ × B→

Therefore, A→ × B→ = - B→ × A→

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Cross product formula
Cross product formula

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