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Cross Product Calculator
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Cross Product Calculator is an online tool which can be used for calculating cross product of two vectors. It takes two vectors and calculates cross product of two vectors and gives the cross product.

Cross Product Calculator for calculating cross product of two vectors 'u' and 'v' where cross product of vectors 'u' and 'v' have to be calculated. If vector 'u' = a i + b j + c k & vector 'v' = d i + e j + f k, put the values of 'a', 'b', 'c', 'd', 'e', 'f' in the calculator and and on click solve, it will calculate cross product of vectors 'u' and 'v'.

## Steps for Calculating the Cross Product

Step 1 :

Define two vectors: Vector u = ai + bj + ck and Vector v = di + ej + fk
where: a, b, c, d, e and f are constants.

Step 2 :

Form the matrix and then calculate the determinant of the matrix

= i(bf - ce) - j(af - cd) + k(ae - bd)

The determinant of the matrix gives the cross product of the vectors u and v.

## Example Problems on Cross Product

1. ### Determine the cross product between x = (2,-4, 5) and y = (6, 8, 5)?

Step 1 :

Given two vectors: Vector x = 2i - 4j + 5k and Vector y = 6i + 8j + 5k

Step 2 :

The cross product =
$\begin{vmatrix} i & j & k \\ 2 & -4 & 5\\ 6 & 8 & 5 \end{vmatrix}$
= i(-4×5 - 5×8) - j(2×5 - 5×6) + k(2×8 + 4×6)
= -60i + 20j + 40k

-60i + 20j + 40k

2. ### Determine the cross product between x = (1,2,-3) and y = (3, -2, 4)?

Step 1 :

Given two vectors: Vector x = 1i + 2j - 3k and Vector y = 3i - 2j + 4k

Step 2 :

The cross product =
$\begin{vmatrix} i & j & k \\ 1 & 2 & -3\\ 3 & -2 & 4 \end{vmatrix}$
= i(2×4 - (-3)×(-2)) - j(1×4 - (-3)×3) + k(1×(-2) - 2×3)
= 2i - 13j - 8k