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

1 Answer
George C.
Jan 2, 2016

#[1,2,1] xx [3,1,-5] = [-11, 8, -5]#

Explanation:

In general:

#[a_x, a_y, a_z] xx [b_x, b_y, b_z]=[abs((a_y, a_z), (b_y, b_z)), abs((a_z, a_z), (b_z, b_x)), abs((a_x, a_y), (b_x, b_y))]#

So:

#[1,2,1] xx [3,1,-5]#

#= [abs((2, 1),(1,-5)), abs((1, 1), (-5, 3)), abs((1, 2),(3,1))]#

#= [(2*-5)-(1*1), (1*3)-(1*-5), (1*1)-(2*3)]#

#= [-10-1, 3+5, 1-6]#

#= [-11, 8, -5]#

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