A vector coplanar with vectores ` hati + hatj and hatj + hatk ` and parallel to the vector ` 2 hati - 2 hatj - 4 hatk `is

A vector coplanar with vectors hati + hatj and hat j + hatk and parallel to the vector 2hati -2 hatj - 4 hatk , is

The vectors which is/are coplanar with vectors hati+hatj+2hatk and hati+2hatj+hatk and perpendicular to the vector hati+hatj+hatk is /are (A) hatj-hatk (B) -hati+hatj (C) hati-hatj (D) -hatj+hatk

The vectors which is/are coplanar with vectors hati+hatj+2hatk and hati+2hatj+hatk and perpendicular to the vector hati+hatj+hatk is /are (A) hatj-hatk (B) -hati+hatj (C) hati-hatj (D) -hatj+hatk

The vectors which is/are coplanar with vectors hati+hatj+2hatk and hati+2hatj+hatk and perpendicular to the vector hati+hatj+hatk is /are (A) hatj-hatk (B) -hati+hatj (C) hati-hatj (D) -hatj+hatk

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))

A plane is parallel to the vectors hati+hatj+hatk and 2hatk and another plane is parallel to the vectors hati+hatj and hati-hatk . The acute angle between the line of intersection of the two planes and the vector hati-hatj+hatk is

A vector of magnitude sqrt2 coplanar with the vectors veca=hati+hatj+2hatk and vecb = hati + 2hatj + hatk, and perpendicular to the vector vecc = hati + hatj +hatk is

A vector of magnitude sqrt2 coplanar with the vectors veca=hati+hatj+2hatk and vecb = hati + hatj + hatk, and perpendicular to the vector vecc = hati + hatj +hatk is