सदिश `hati+hatj+hatk` का सदिश `hati+hatj` की दिशा में घटक ज्ञात कीजिए

The projection of hati-hatj+hatk on hati-hatj is :

The value of [hati - hatj , hatj - hatk, hatk - hati] is :

Why is hati.hatj=hatj.hatk=hatk.hati=0

A unit vector coplanar with hati + hatj + 2 hatk and hati + 2 hatj + hatk, and perpendicular to hati + hatj + hatk is : a) ((hatj - hatk )/( sqrt2)) b) ((hati + hatj+ hatk )/( sqrt3)) c) ((hati + hatj + 2 hatk )/( sqrt6)) d) ((hati + 2 hatj + hatk )/( sqrt6))

Vectors Perpendicular to hati - hatj- hatk and in the plane of hati + hatj + hatk and - hati + hatj + hatk are