# What is the cross product of <-3,0,1> and <3,-6,4>?

Feb 2, 2016

$\left[6 , 15 , 18\right]$

#### Explanation:

The cross product of two vectors is also a vector. If vector $\vec{a} = \left[a 1 , a 2 , a 3\right]$ and vector $\vec{b} = \left[b 1 , b 2 , b 3\right]$ then the components of the cross product vector $\vec{v} = \vec{a} \times \vec{b}$ can be calculated from

${v}_{1} = {a}_{2} {b}_{3} - {a}_{3} {b}_{2}$
${v}_{2} = {a}_{3} {b}_{1} - {a}_{1} {b}_{3}$
${v}_{3} = {a}_{1} {b}_{2} - {a}_{2} {b}_{1}$

The best way to memorise these terms is to express the two vectors as a determinant and study the pattern of math operations that will yield the same vector components. If want to compute vector products really fast then you will need to write a short computer program or punch in the formulas in a Spreadsheet.