Two vectors `vecalpha=3hati+4hatj and vecbeta=5hati+2hatj-14hatk` have the same initial point then their angulr bisector having magnitude `7/3` be (A) `7/(3sqrt(6))(2hati+hatj-hatk)` (B) `7/(3sqrt(3))(\hati+hatj-hatk)` (C) `7/(3sqrt(3))(hati-hatj+hatk)` (D) `7/(3sqrt(3))(hati-hatj-hatk)`

A unit vector which is equally inclined to the vector hati, (-2hati+hatj+2hatk)/3 and (-4hatj-3hatk)/5 (A) 1/sqrt(51)(-hati+5hatj-5hatk) (B) 1/sqrt(51)(hati-5hatj+5hatk) (C) 1/sqrt(51)(hati+5hatj-5hatk) (D) 1/sqrt(51)(hati+5hatj+5hatk)

A line passes through the points whose position vectors are hati+hatj-2hatk and hati-3hatj+hatk . The position vector of a point on it at unit distance from the first point is (A) (1)/(5)(5hati+hatj-7hatk) (B) (1)/(5)(5hati+9hatj-13hatk) (C) (hati-4hatj+3hatk) (D) (1)/(5)(hati-4hatj+3hatk)

A vector vecv or magnitude 4 units is equally inclined to the vectors hati+hatj, hatj+hatk, hatk+hati, which of the following is correct? (A) vecv=4/sqrt(3)(hati-hatj-hatk) (B) vecv=4/sqrt(3)(hati+hatj-hatk) (C) vecv=4/sqrt(3)(hati+hatj+hatk) (D) vecv=4(hati+hatj+hatk)

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

Let veca=2hati+hatj+hatk, vecb=hati+2hatj-hatk and vecc=hati+hatj-2hatk be three vectors . A vector in the plane 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

A vector of magnitude 2 along a bisector of the angle between the two vectors 2hati-2hatj+hatk and hati+2hatj-2hatk is (A) 2/sqrt(10)(3hati-hatk) (B) 2/sqrt(23)(hati-3hatj+3hatk) (C) 1/sqrt(26) (hati-4hatj+3hatk) (D) none of these

Let vecb=-veci+4vecj+6veck, vecc=2veci-7vecj-10veck. If veca be a unit vector and the scalar triple product [veca vecb vecc] has the greatest value then veca is A. (1)/(sqrt(3))(hati+hatj+hatk) B. (1)/(sqrt(5))(sqrt(2)hati-hatj-sqrt(2)hatk) C. (1)/(3)(2hati+2hatj-hatk) D. (1)/(sqrt(59))(3hati-7hatj-hatk)

If vec a =hati +3hatj , vecb = 2hati -hatj - hatk and vec c =mhati +7 hatj +3hatk are coplanar then find the value of m.

If a=3hati-2hatj+hatk,b=2hati-4hatj-3hatk and c=-hati+2hatj+2hatk , then a+b+c is

If p=7hati-2hatj+3hatk and q=3hati+hatj+5hatk , then find the magnitude of p-2q.