Triple Vector Product

In math, 3d vector is a vector with 3 dimensions. For example, 2`veci` + 2`vecj` + 4`veck` is a 3d vector. Cross product of a 3d vector gives resultant vector perpendicular to the two given vectors. A general formula is available for finding the cross product of 3d vectors. Let us study the explanation of 3d vector cross product with examples.

Let us take the following Triple Vector Product

a = a1 `veci ` + a2 `vecj` + a3 `veck ` and b = b1 `veci` + b2 `vecj` + b3 `veck`

Now, the cross product of the above two 3D vectors is as follows.

a x b = `|[veci,vecj, veck],[a_1,a_2, a_3],[b_1, b_2, b_3]|`

a x b = `veci` (a2b3 - a3b2) - `vecj` (a1b3 - a3b1) + `veck`(a1b3 - a3b1)

By using the above general description, we can find the cross product of two given 3D vectors.Looking out for more help on Algebra Tutor in algebra by visiting listed websites.

Derivation of cross product:

a x b = (a1 b1) `veci` + (a1 b2) `veci ` `vecj` + (a1 b3) `veci` `veck ` +

(a2 b1) `vecj ` `veci` + (a2 b2) `vecj` `vecj` + (a2 b3) `vecj` ` veck` +

(a3 b1) `veck`` veci` + (a3 b2)` veck` `vecj` + (a3 b2) `veck` `veck`

Some terms related to cross product:

`veci` x `vecj` = `veck`

`vecj` x `vec k` =` veci`

`veck` x `veci` =` vecj`

`vecj` x `veci` = -`veck`

`veck` x `vecj` = - `veci`

`veci ` x `veck` = -`vecj`

Based on the above terms, the formula of cross product becomes,

a x b = `veci` (a2b3 - a3b2) - `vecj` (a1b3 - a3b1) + `veck`(a1b3 - a3b1)