A unit vector `hata` makes an angle `pi/4` with z-axis, `if hata+hati+hatj` is a unit vector then `hata` is equal to (A) `hati+hatj+hatk/2` (B) `hati/2+hatj/2-hatk/sqrt(2)` (C) `-hati/2-hatj/2+hatk/sqrt(2)` (D) `hati/2-hatj/2-hatk/sqrt(2)`

Find a unit vector perpendicular to both the vectors hati-2hatj+hatk and hati+2hatj+hatk .

Find a unit vector in the diection of the vector. (i) (3hati + 4hatj - 5hatk) , (ii) (3hati - 2hatj + 6hatk) (iii) (hati + hatk) , (iv) (2hati + hatj + 2hatk)

Find a unit vector perpendicular to each of the vectors hati+2hatj-3hatk and hati-2hatj+hatk .

If the vectors hati-hatj, hatj+hatk and veca form a triangle then veca may be (A) -hati-hatk (B) hati-2hatj-hatk (C) 2hati+hatj+hatjk (D) hati+hatk

A unit vector int eh plane of the vectors 2hati+hatj+hatk, hati-hatj+hatk and orthogonal to 5hati+2hatj-6hatk is (A) (6hati-5hatk)/sqrt(6) (B) (3hatj-hatk)/sqrt(10) (C) (hati-5hatj)/sqrt(29) (D) (2hati+hatj-2hatk)/3

Fina a unit vector in the direaction of the resultant of the vectors hati - hatj + 3hatk, 2 hati + hatj- 2 hatk and hati + 2 hatj- 2 hatk.

The unit vector which is orthogonal to the vector 3hati+2hatj+6hatk and is coplanar with the vectors 2hati+hatj+hatk and hati-hatj+hatk is (A) (2hati-6hatj+hatk)/sqrt(41) (B) (2hati-3hatj)/sqrt(3) (C) 3hatj-hatk)/sqrt(10) (D) (4hati+3hatj-3hatk)/sqrt(34)

The unit vector parallel to the resultant vector of 2hati+4hatj-5hatk and hati+2hatj+3hatk is

Find a unit vector perpendicular to both the vectors 2hati+3hatj+hatk) and (hati-hatj+2hatk) .