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)#.