If `hata=hati+2hatj+3hatk, hatb=hatixx(vecaxxhati)+hatjxx(vecaxxhatj)+hatkxx(vecaxxhatk)` then length of `vecb` is equal to (A) `sqrt(12)` (B) `2sqrt(12)` (C) `2sqrt(14)` (D) `3sqrt(12)`

10sqrt(12) -: 2sqrt(3)

1/(sqrt(9)-\ sqrt(8)) is equal to: (a) 3+2sqrt(2) (b) 1/(3+2sqrt(2)) (c) 3-2sqrt(2) (d) 3/2-\ sqrt(2)

If the vectors vec(PQ)=-3hati+4hatj+4hatk and vec(PR)=5hati-2hatj+4hatk are the sides of a triangle PQR, then the length o the median through P is (A) sqrt(14) (B) sqrt(15) (C) sqrt(17) (D) sqrt(18)

The rationalisation factor of sqrt(3) is (a) -sqrt(3) (b) 1/(sqrt(3)) (c) 2sqrt(3) (d) -2sqrt(3)

If the vectors vec(AB)=3hati+4hatk and vec(AC)=5hati-2hatj+4hatk are the sides of a triangle ABC, then the length of the median through A is (A) sqrt(33) (B) sqrt(45) (C) sqrt(18) (D) sqrt(720

The vector vec(AB)=3hati+4hatk and vec(AC)=5hati-2hatj+4hatk are sides of a triangle ABC. The length of the median through A is (A) sqrt(18) (B) sqrt(72) (C) sqrt(33) (D) sqrt(288)

The rationalisation factor of 2+sqrt(3) is (a) 2-sqrt(3) (b) sqrt(2)+3 (c) sqrt(2)-3 (d) sqrt(3)-2

The projection of the vector 2hati+ahatj-hatk on the vector hati-2hatj+hatk is -5/sqrt(6) then the value of a is equal to (A) 1 (B) 2 (C) -2 (D) 3

If veca is any vector and hati,hatj and hatk are unit vectors along the x,y and z directions then hatixx(vecaxxhati)+hatjxx(vecaxxhatj)+hatkxx(vecaxxveck)= (A) veca (B) -veca (C) 2veca (D) 0

If veca is perpendicuar to vecb and vecc |veca|=2, |vecb|=3,|vecc|=4 and the angle between vecb and vecc is (2pi)/3, then [veca vecb vecc] is equal to (A) 4sqrt(3) (B) 6sqrt(3) (C) 12sqrt(3) (D) 18sqrt(3)