It sounds like you're referring to a formula related to vectors, and you're wondering if it's the same as the cross product formula.

Let's clarify: The cross product (also called the vector product) is a way to multiply two vectors in three-dimensional space. The formula for the cross product of vectors A = (a₁, a₂, a₃) and B = (b₁, b₂, b₃) is:

$\mathbf{A} \times \mathbf{B} = (a_2b_3 - a_3b_2, a_3b_1 - a_1b_3, a_1b_2 - a_2b_1)$

This gives a new vector that is perpendicular to both A and B, and its magnitude is given by:

$|\mathbf{A} \times \mathbf{B}| = |\mathbf{A}| |\mathbf{B}| \sin(\theta)$

where $\theta$ is the angle between the two vectors.

Is it the same as another formula?

The answer depends on which formula you're comparing it to. If you're thinking of the determinant of a 3x3 matrix involving vectors (which is used for the cross product), then yes, they are essentially the same thing, since the cross product can be computed using the determinant of a matrix with the unit vectors i, j, k as the first row and the components of vectors A and B as the second and third rows:

\mathbf{i} & \mathbf{j} & \mathbf{k} \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \end{vmatrix}$$ But if you're referring to a different formula (like one for dot products, magnitudes, or angles), then that might be different. Let me know if you'd like more detail on a specific formula!