# What is the cross product of #[-1, -1, 2]# and #[-1, 2, 2] #?

##### 1 Answer

#### Answer:

#### Explanation:

The cross product between two vectors

where

For of the unit vectors

#color(white)( (color(black){hati xx hati = vec0}, color(black){qquad hati xx hatj = hatk}, color(black){qquad hati xx hatk = -hatj}), (color(black){hatj xx hati = -hatk}, color(black){qquad hatj xx hatj = vec0}, color(black){qquad hatj xx hatk = hati}), (color(black){hatk xx hati = hatj}, color(black){qquad hatk xx hatj = -hati}, color(black){qquad hatk xx hatk = vec0}))#

Also, note that cross product is distributive.

#vecA xx (vecB + vecC) = vecA xx vecB + vecA xx vecC# .

So for this question.

#[-1,-1,2] xx [-1,2,2]#

#= (-hati - hatj + 2hatk) xx (-hati + 2hatj + 2hatk)#

#= color(white)( (color(black){-hati xx (-hati) - hati xx 2hatj - hati xx 2hatk}), (color(black){-hatj xx (-hati) - hatj xx 2hatj - hatj xx 2hatk}), (color(black){+2hatk xx (-hati) + 2hatk xx 2hatj + 2hatk xx 2hatk}) )#

#= color(white)( (color(black){vec0 - 2hatk quad qquad + 2hatj}), (color(black){-hatk - 2(vec0) - 2hati}), (color(black){- 2hatj - 4hati quad - 4(vec0)}) )#

#= -6hati - 3hatk#

#= [-6,0,-3]#