(6i + -3j + 6k) x (8i + 2j + -9k)

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Given the following two vectors in R³:
calculate the cross product X × Y

X = 6i - 3j + 6k

Y = 8i + 2j - 9k

Write the coefficients as a matrix

Evaluate Cross Product Formula

X × Y = (x₂y₃ - x₃y₂)i + (x₃y₁ - x₁y₃)j + (x₁y₂ - x₂y₁)k

X × Y = (-3 x -9 - 6 x 2)i + (6 x 8 - 6 x -9)j + (6 x 2 - -3 x 8)k

X × Y = (27 - 12)i + (48 - -54)j + (12 - -24)k

X × Y = 15i + 102j + 36k

Parallel Check:

Since X × Y <> 0:
X and Y are not parallel

Final Answer