Show that each of the given three vectors is a unit vector. `(1)/(7)(2hati+3hatj+6hatk),(1)/(7)(3hati-6hatj+2hatk),(1)/(7)(6hati+2hatj-3hatk)`
Also , show that they are mutually perpendicular to each other.

find the projection of the vector hati-3hatj-7hatk on the vector 7hati-hatj-8 hatk

Find the projection of the vector hati+3hatj+7hatk on the vector 7hati-hatj+8hatk .

find the projection of the vector hati+2hatj+3hatk on the vector 5hati-2hatj+4 hatk

Find the modulus of the Vector 1/3 (2hati - 2hatj +hatk) is

Find the angle between the vectors hati-2hatj+3hatkand3hati-2hatj+hatk

Find the angle between the following pairs of vectors 3hati+2hatj-6hatk, 4hati-3hatj+hatk , hati-2hatj+3hatk, 3hati-2hatj+hatk

Statement 1: If a_(1)hati + a_(2)hatj + a_(3)hatk, vecbhati+b_(2)hatj + b_(3) hatk and c_(1)hati + c_(2)hatj + c_(3)hatk are three mutually perpendicular unit vectors then a_(1)hati + b_(1)hatj + c_(1)hatk,a_(2)hati +b_(2)hatj+c_(2) hatk and a_(3)hati + b_(3) hatj + c_(3) hatk may be mutually perpendicular unit vectors. Statement 2 : value of determinant and its transpose are the same.

The vectors (29)/(3)hati-4hatj+5hatk, 2hati+mhatj+hatk and veci+2hatj+hatk are coplanar, find m.

A vector perpendicular to both of (3hati+hatj+2hatk) and (2hati-2hatj+4hatk) is