If `a=hati+hatj+hatk and b=hati-hatj`, then vectors `((a*hati)hati+(a*hatj)hatj+(a*hatk)hatk),{(b*hati)hati+(bhatj)hatj+(b*hatk)hatk} and( hati+hatj-2hatk)`

(a*hati)hati+(a*hatj)hatj+(a*hatk)hatk is equal to

If a=hati+hatj+hatk,b=hati+hatj-hatk , then vectors perpendicular to a and b is/are

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

Find the direction cosines of the resultant of the vectors (hati+hatj+hatk),(-hati+hatj+hatk),(hati-hatj+hatk) and (hati+hatj-hatk) .

The unit vector which is orthogonal to the vector 5hati + 2hatj + 6hatk and is coplanar with vectors 2hati + hatj + hatk and hati - hatj + hatk is (a) (2hati - 6hatj + hatk)/sqrt41 (b) (2hati-3hatj)/sqrt13 (c) (3 hatj -hatk)/sqrt10 (d) (4hati + 3hatj - 3hatk)/sqrt34

The value of hati.(hatj xx hatk) + hatj.(hati xx hatk) + hatk.( hati xx hatj) is

If veca=(hati+hatj+hatk), and veca.vecb=1 and vecaxxvecb = -(hati-hatk) then vecb is (A) hati-hatj+hatk (B) 2hatj-hatk (C) hatj (D) 2hati

If veca = (hati + hatj +hatk), veca. vecb= 1 and vecaxxvecb = hatj -hatk , " then " vecb is (a) hati - hatj + hatk (b) 2hati - hatk (c) hati (d) 2hati

The position vector of the pont where the line vecr=hati-j+hatk+t(hati+hatj-hatk) meets plane vecr.(hati+hatj+hatk)=5 is (A) 5hati+hatj-hatk (B) 5hati+3hatj-3hatk (C) 5hati+hatj+hatk (D) 4hati+2hatj-2hatk

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