Problem

The key is recognizing that the scalar triple product $\mathbf{A} \cdot (\mathbf{B} \times \mathbf{C})$ measures the signed volume of the parallelepiped formed by three vectors. You'll compute the cross product $\mathbf{B} \times \mathbf{C}$ first (which gives a vector perpendicular to both), then take its dot product with $\mathbf{A}$. Alternatively, use the determinant formula directly—it's often faster and less error-prone.

The key is recognizing that the scalar triple product $\mathbf{A} \cdot (\mathbf{B} \times \mathbf{C})$ measures the signed volume of the parallelepiped formed by three vectors. You'll compute the cross product $\mathbf{B} \times \mathbf{C}$ first (which gives a vector perpendicular to both), then take its dot product with $\mathbf{A}$. Alternatively, use the determinant formula directly—it's often faster and less error-prone.