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
i
j
k
x1
x2
x3
y1
y2
y3
→
i
j
k
6
-3
6
8
2
-9
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
X × Y = 15i + 102j + 36k Since X × Y <> 0: X and Y are not parallel
What is the Answer?
X × Y = 15i + 102j + 36k Since X × Y <> 0: X and Y are not parallel
How does the Cross Product Calculator work?
Free Cross Product Calculator - Given two vectors A and B in R3, this calculates the cross product A × B as well as determine if the two vectors are parallel This calculator has 6 inputs.
What 1 formula is used for the Cross Product Calculator?