Find the projection of :
(i) `hati-hatj` on Z-axis (ii) `hati+2hatj-2hatk` on `2hati-hatj+5hatk` (iii) `3hati+hatj-hatk` on `4hati-hatj+2hatk`

Vectors perpendicular to hati-hatj-hatk and in the plane of hati+hatj+hatk and -hati+hatj+hatk are (A) hati+hatk (B) 2hati+hatj+hatk (C) 3hati+2hatj+hatk (D) -4hati-2hatj-2hatk

Let veca=2hati=hatj+hatk, vecb=hati+2hatj-hatk and vecc=hati+hatj-2hatk be three vectors . A vector in the pland of vecb and vecc whose projection on veca is of magnitude sqrt((2/3)) is (A) 2hati+3hatj+3hatk (B) 2hati+3hatj-3hatk (C) -2hati-hatj+5hatk (D) 2hati+hatj+5hatk

Show that the vectors hati+2hatj-3hatk , 2hati-hatj+2hatk and 3hati+hatj-hatk are coplanar.

Find the projection of the vector hati+3hatj+7hatk on the vector 2hati+6hatj+3hatk .

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

Prove that points hati+2hatj-3hatk, 2hati-hatj+hatk and 2hati+5hatj-hatk form a triangle in space.