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

1 Answer
Burglar
Jun 13, 2016

It is (-5, -10, -5)(−5,−10,−5).

Explanation:

Given two vectors v_1=(x_1, y_1, z_1)v1=(x1,y1,z1) and v_2=(x_2, y_2, z_2)v2=(x2,y2,z2) the cross product

v_1\times v_2v1×v2 is given by

v_1\times v_2=(y_1z_2-z_1y_2, z_1x_2-x_1z_2, x_1y_2-x_2y_1)v1×v2=(y1z2−z1y2,z1x2−x1z2,x1y2−x2y1).

For your two vectors it is

(4, -3, 2)\times(1, -2, 3)(4,−3,2)×(1,−2,3)
=(-3*3-2*(-2), 2*1-4*3, 4*(-2)-(-3)*1)=(−3⋅3−2⋅(−2),2⋅1−4⋅3,4⋅(−2)−(−3)⋅1)
=(-9+4, 2-12, -8+3)=(−9+4,2−12,−8+3)
=(-5, -10, -5)=(−5,−10,−5).

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