What is the cross product of $[1, -4, 0]$ and $[4,3,6]$ ?

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Answer 1 · 2016-06-01T12:45:22

It is $(-24, -6, 19)$ .

The cross product of two vectors with coordinates

$v_1=(x_1, y_1, z_1)$
$v_2=(x_2, y_2, z_2)$

is defined as

$v_1\timesv_2=(y_1z_2-z_1y_2, z_1x_2-x_1z_2, x_1y_2-y_1x_2)$

We can apply this to our case

$v_1=(1, -4, 0)$
$v_2=(4,3,6)$

$v_1\times v_2=(-4*6-0*3, 0*4-1*6, 1*3-(-4)*4)$
$=(-24, -6, 19)$ .

What is the cross product of [1, -4, 0][1, -4, 0] and [4,3,6] [4,3,6] ?