Question

With respect to a right handed Cartesian coordinate system and given that . A = 4i + k and B = 2i + j _ 3k find A cross B

Answer 1

Using the left-hand rule,

$(4\,\vec\imath+\vec k)\times(2\,\vec\imath+\vec\jmath-3\,\vec k) = \begin{vmatrix}\vec\imath&\vec\jmath&\vec k\\4&0&1\\2&1&-3\end{vmatrix} = -\vec\imath+14\,\vec\jmath+4\,\vec k$

Then in the right-handed rectangular coordinates, the cross product is the negative of this,

$\boxed{\vec\imath-14\,\vec\jmath-4\,\vec k}$