3D geometry

[jatjoh]

Show that the three lines with direction cosines 12/13 ,-3/13 ,-4/13 ;
4/13 ,12/13 ,3/13 ; 3/13 ,-4/13 ,12/13 are mutually perpendicular..

hi im a new member....i wud like to know do we take the dot product n prove this..thanks!

 

[tkhunny]

That certainly is the easy way. You can do it harder ways if you like.

Let's see what you get. What about the Dot Product tells us anything about perpendicularity?

 

[jatjoh]

i know dot product of two perpendicular vectors is zero,but i dont know how to prove this for the sum,,if i was explained how to do this using this step or any other step it would be helpful..thanks

 

[tkhunny]

\(\displaystyle A \perp B\)

\(\displaystyle A \perp C\)

\(\displaystyle B \perp C\)

Done?