Cross products of two vectors
Vector product of two non-parallel vectors is a vector perpendicular to both the vectors. If \(\vec{a}\) and \(\vec{b}\) are non-parallel vectors then \(\vec{a} \times \vec{b}\) is their cross product - a vector making 90 degree angle with both \(\vec{a}\) and \(\vec{b}\). It is also known as cross product. Another way to think of it is to imagine a plane “containing” the two non-parallel vectors. The vector product makes a 90 degree angle with the plane containing them, i.e. it is a vector normal to the plane . Let \(\vec{a} = a_{1} \hat{i} + a_{2} \hat{j} + a_{3} \hat{k}\) and, \(\vec{b} = b_{1} \hat{i} + b_{2} \hat{j} + b_{3} \hat{k}\) Then, \(\vec{a} \times \vec{b}\) is equal to the following determinant : \(\vec{a} \times \vec{b} = \Biggl|\matrix{\hat{i} & \hat{j} & \hat{k} \\ a_{1} & a_{2} & a_{3} \\ b_{1} & b_{2} & b_{3}}\Biggl|\) The first row are the unit vectors \(\hat{i}, \hat{j}, \hat{k}...