How to Calculate Cross Product of Two Vectors?

Consider that we are given two vectors

Vector, \(V_1 = a_1 \vec{i} + b_1 \vec{j} + c_1 \vec{k}\)

Vector, \(V_2 = a_2 \vec{i} + b_2 \vec{j} + c_2 \vec{k}\)

The cross project of the two vectors can be denoted in terms of matrix determinant, as shown in the following.

\( V_1 \times V_2 = \begin{vmatrix}\vec{i} & \vec{j} & \vec{k}\\a_1 & b_1 & c_1\\a_2 & b_2 & c_2\end{vmatrix} \)

To find the cross product of the given two vectors, use the following formula.

Result Vector, \(V_1 \times V_2 = (b_1 c_2 - b_2 c_1)\vec{i} - (a_1 c_2 - a_2 c_1)\vec{j} + (a_1 b_2 - a_2 b_1)\vec{k} \)