Volume of the parallelepiped having vertices at O≡(0,0,0),A≡(2,–2,1),B≡(5,–4,4)and c≡(1,–2,4) is
5 cuunits
10 cuunits
15 cuunits
20 cuunits
Explanation for correct option
Volume of parallelepiped:Given vertices O≡(0,0,0),A≡(2,–2,1),B≡(5,–4,4)and c≡(1,–2,4) OA→=(2-0)i^+(-2-0)j^+(1-0)k^=2i^-2j^+k^Similarly, OB→=5i^-4j^+4k^&OC→=i^-2j^+4k^Volume of parallelepiped =[OA→OB→OC→] =2-215-441-24=2(-16+8)+2(20-4)+1(-10+4)=-16+32-6=10cuunits
Hence option(B) is correct.