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

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 = 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




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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?

X × Y = (x2y3 - x3y2)i + (x3y1x1y3)j + (x12x2y1)k

For more math formulas, check out our Formula Dossier

What 4 concepts are covered in the Cross Product Calculator?

cross product
a binary operation on two vectors in a three-dimensional oriented Euclidean vector space
formula
a fact or a rule written with mathematical symbols. A concise way of expressing information symbolically.
parallel
vector
directed line segment

Example calculations for the Cross Product Calculator

  1. 8i-j+3k x 5i+j-9k
  2. 6i-3j+6k * 8i+2j-9k
  3. (8i-2j+13k)(3i+5j-k)

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