Vectors

Vector Product of Vectors

Keywords: multiplication of vectors, vector product

 

Vector Product of Vectors

a = x 1 i + y 1 j + z 1 k , b = x 2 i + y 2 j + z 2 k
c a c b
c = a × b = | i j k x 1 y 1 z 1 x 2 y 2 z 2 |
c = ( y 1 z 2 z 1 y 2 ) i + ( z 1 x 2 x 1 z 2 ) j + ( x 1 y 2 y 1 x 2 ) k
| c | = | a | · | b | · s i n α

The result of vector product, vector c⃗, has a length that is equal with the area of parallelogram between vecrors a⃗ and b⃗ (pink area).