Enter x1i + x2j + x3k

 i  j  k

Enter y1i + y2j + y3k

 i  i  k
  

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

X = 8i - 2j + 13k

Y = 3i + 5j - k

Write the coefficients as a matrix

 i  j  k 
 x1  x2  x3 
 y1  y2  y3 
 → 
 i  j  k 
 8  -2  13 
 3  5  -1 

Evaluate Cross Product Formula

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

X × Y = (-2 x -1 - 13 x 5)i + (13 x 3 - 8 x -1)j + (8 x 5 - -2 x 3)k

X × Y = (2 - 65)i + (39 - -8)j + (40 - -6)k

X × Y = - 63i + 47j + 46k

Parallel Check:

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

Final Answer


X × Y = - 63i + 47j + 46k
Since X × Y <> 0:
X and Y are not parallel