R3 – Multiplication – Cross Product

Cross product multiplication in R3 uses the same approach as in classical mathematics.

The cross product of the points $a (a_x, a_y, a_z)$ and $b (b_x, b_y, b_z)$ is written as $a \times b$ and is given by the formula:

$a \times b = ((a_y*b_z + a_z*b_y), (a_z*b_x + a_x*b_z),( a_x*b_y + a_y*b_x))$

Unlike for dot-product, the Opposite Signs are used in multiplication. For example:

- $= ((5i^v { }*3j^v + 6j\hat{ } { }*2i\hat{ }), (6j\hat{ }*1^v + 4^v*3j^v), (4^v*2i\hat{ } + 5i^v { }*1^v))$
- $= (( 15^v + 12\hat { }), ( 6i^v { } + 12i^v), ( 8j^v + 6j^v))$
- $= (3^v, 6i^v, 2j\hat { })$

$(6.3^v + 4.7i\hat { } + 5.3j\hat { }) \times (3.9\hat { } + 7.5i^v + 2.4j^v)$
$= ((4.7i\hat { }*2.4j^v + 5.3j\hat { }*7.5i^v), (5.3j\hat { }*3.9\hat { } + 6.3^v*2.4j^v), (6.3^v*7.5i^v + 4.7i\hat { }*3.9\hat { }))$
$= (( 11.28^v + 39.75\hat { }), ( 20.67i\hat { } + 15.12i^v), ( 47.25j\hat { } + 18.33j^v))$
$= (28.47\hat { }, 5.55i\hat { }, 28.92j\hat { })$

Conclusion

Try this example of R3 cross product multiplication with our online calculator.

Share to: