If the sides `vec(AB)` of an equilateral triangle ABC lying in the xy-plane is `3hati` then the side `vec(CB)` can be (A) `-3/2(hati-sqrt(3))` (B) `3/2(hati-sqrt(3))` (C) `-3/2(hati+sqrt(3))` (D) `3/2(hati+sqrt(3))`

If side vec AB of an equilateral trangle ABC lying in the x-y plane 3hat i ,then side vec CB can be -(3)/(2)(hat i-sqrt(3)hat j) b.-(3)/(2)(hat i-sqrt(3)hat j) c.-(3)/(2)(hat i+sqrt(3)hat j) d.(3)/(2)(hat i+sqrt(3)hat j)

veca=hati-hatj+hatk and vecb=2hati+4hati+3hatk are one of the sides and medians respectively of a triangle through the same vertex, then area of the triangle is (A) 1/2 sqrt(83) (B) sqrt(83) (C) 1/2 sqrt(85) (D) sqrt(86)

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)

If the work done by a force vecF=hati+hatj-8hatk along a givne vector in the xy-plane is 8 units and the magnitude of the given vector is 4sqrt(3) then the given vector is represented as (A) (4+2sqrt(2))hati+(4-2sqrt(2))hatj (B) (4hati+3sqrt(2)hatj) (C) (4sqrt(2)hati+4hatj) (D) (4+2sqrt(2))(hati+hatj)

The vectors vec(AB)=3hati+4hatk and vec(AC)=5hati-2hatj+4hatk are the sides of a triangle ABC. The length of the median through A is (A) sqrt(72) (B) sqrt(33) (C) sqrt(2880 (D) sqrt(18)

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

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(18) (B) sqrt(72) (C) sqrt(33) (D) sqrt(45)

The vector (s) equally inclined to the vectors hati-hatj+hatk and hati+hatj-hatk in the plane containing them is (are_ (A) (hati+hatj+hatk)/sqrt(3) (B) hati (C) hati+hatk (D) hati-hatk

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)

If vec(A) = 3 hati +2hatj and vec(B) = hati - 2hatj +3hatk , find the magnitudes of vec(A) +vec(B) and vec(A) - vec(B) .