What is the cross product of [4,-3,2] and [3,1,-5] ?

Dec 14, 2015

$= \left[13 , 26 , 13\right]$

Explanation:

The rule for cross products states that for two vectors, $\vec{a} = \left[{a}_{1} , {a}_{2} , {a}_{3}\right]$ and $\vec{b} = \left[{b}_{1} , {b}_{2} , {b}_{3}\right]$;

$\vec{a} \times \vec{b} = \left[{a}_{2} {b}_{3} - {a}_{3} {b}_{2} , {a}_{3} {b}_{1} - {b}_{3} {a}_{1} , {a}_{1} {b}_{2} - {a}_{2} {b}_{1}\right]$

For the two vectors given, this means that;

[4, ~3, 2] xx [3, 1, ~5]

= [(~3)(~5)-(2)(1), (2)(3) - (~5)(4), (4)(1)-(~3)(3) ]

$= \left[15 - 2 , 6 + 20 , 4 + 9\right]$

$= \left[13 , 26 , 13\right]$