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

X = 8i - j + 3k

Y = 5i + j - 9k

Write the coefficients as a matrix

 i  j  k 
 x1  x2  x3 
 y1  y2  y3 
 → 
 i  j  k 
 8  -1  3 
 5  1  -9 

Evaluate Cross Product Formula

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

X × Y = (-1 x -9 - 3 x 1)i + (3 x 5 - 8 x -9)j + (8 x 1 - -1 x 5)k

X × Y = (9 - 3)i + (15 - -72)j + (8 - -5)k

X × Y = 6i + 87j + 13k

Parallel Check:

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

Final Answer


X × Y = 6i + 87j + 13k
Since X × Y <> 0:
X and Y are not parallel

An Automated Online Math Tutor serving 8.1 million parents and students in 235 countries and territories.

Our Services
Top Categories
Community