Why is the cross product a × b negative?

[tony873004]

find the cross product a x b of the vectors a = 5.0m,i and b=4.3m,k
$$5.0m\ast 4.3m\ast \sin (90)=22m^2,\hat {j}$$

The back of the book gives
$$-(22m^2)\hat {j}$$

Where does the minus sign come from?

 

[dextercioby]

Naturally

$$\vec{i}\times\vec{k}=-\vec{j}$$

,because

$$\vec{k}\times\vec{i}=\vec{j}$$

Daniel.

 

[tony873004]

thanks, dextercioby

 

[HallsofIvy]

Or: "right hand rule". Curl the fingers of your right hand from the positive x-axis (i) to the positive z-axis "j". You thumb will be pointing down the negative y-axis.