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
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
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.
This calculator has 6 inputs.
What 1 formula is used for the Cross Product Calculator?
X × Y = (x2y3 - x3y2)i + (x3y1x1y3)j + (x12x2y1)k
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
