The formula to calculate the cross product of two vectors is:
\[ \mathbf{a} \times \mathbf{b} = (a_2 b_3 - a_3 b_2, a_3 b_1 - a_1 b_3, a_1 b_2 - a_2 b_1) \]
Where:
A cross product, also known as a vector product, is a mathematical operation in which the result of the cross product between two vectors is a new vector that is perpendicular to both vectors. The magnitude of this new vector is equal to the area of a parallelogram with sides of the two original vectors. The cross product is not to be confused with the dot product which is a simpler algebraic operation that returns a single number as opposed to a new vector.
Let's assume the following:
Step 1: Calculate the cross product:
\[ \mathbf{a} \times \mathbf{b} = (2 \cdot 6 - 3 \cdot 5, 3 \cdot 4 - 1 \cdot 6, 1 \cdot 5 - 2 \cdot 4) = (-3, 6, -3) \]
Therefore, the cross product is \((-3, 6, -3)\).
