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Given the following two vectors in R³:
calculate the cross product X × Y
X = 2i + j + 2k
Y = 3i - j - 3k

Write the coefficients as a matrix

i	j	k
x1	x2	x3
y1	y2	y3

i	j	k
2	1	2
3	-1	-3

Evaluate Cross Product Formula

X × Y = (x₂y₃ - x₃y₂)i + (x₃y₁ - x₁y₃)j + (x₁y₂ - x₂y₁)k
X × Y = (1 x -3 - 2 x -1)i + (2 x 3 - 2 x -3)j + (2 x -1 - 1 x 3)k
X × Y = (-3 - -2)i + (6 - -6)j + (-2 - 3)k
X × Y = - i + 12j - 5k