What is the cross product of $[1, -2, -3]$ and $[2, -5, 8]$ ?

Question

1753 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-07T17:43:31

The answer is $=〈-31,-14,-1〉$

The cross product of 2 vectors

$veca=〈a_1,a_2,a_3〉$

and $vecb=〈b_1,b_2b_3〉$

is given by

the determinant $| (hati,hatj,hatk), (a_1,a_2,a_3), (b_1,b_2,b_3) |$

$=hati(a_2b_3-a_3b_2)-hatj(a_1b_3-a_3b_1)+hatk(a_1b_2-a_2b_1)$

Here we have,

$〈1.-2-3〉$ and $〈2,-5,8〉$

So, the cross product is

$| (hati,hatj,hatk), (1,-2,-3), (2,-5,8) |$

$=hati(-16-15)-hatj(8+6)+hatk(-5+4)$

$=〈-31,-14,-1〉$

Verification (the dot product of perpendicular vectors is $=0$ )

$〈-31,-14,-1〉.〈1.-2-3〉=-31+28+3=0$

$〈-31,-14,-1〉.〈2,-5,8〉=-62+70-8=0$

What is the cross product of [1, -2, -3][1, -2, -3] and [2, -5, 8] [2, -5, 8] ?