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

Enter x1i + x2j + x3k

 i  j  k

Enter y1i + y2j + y3k

 i  i  k
  

Answer
X × Y = 15i + 102j + 36k
Since X × Y <> 0:
X and Y are not parallel

↓Steps Explained:↓



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

Final Answer

X × Y = 15i + 102j + 36k
Since X × Y <> 0:
X and Y are not parallel


Related Calculators:  Markov Chain  |  Plane and Parametric Equations in R3  |  Sum to Product and Product to Sum Formulas
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