Let `vecV = 2hati +hatj - hatk and vecW= hati + 3hatk . if vecU` is a unit vector, then the maximum value of the scalar triple product `[ vecU vecV vecW]` is

If vector vecP=a hati + a hatj +3hatk and vecQ=a hati -2 hatj -hatk are perpendicular to each other , then the positive value of a is

Let vecu=2hati-hatj+hatk, vecv=-3hatj+2hatk be vectors and vecw be a unit vector in the xy-plane. Then the maximum possible value of |(vecu xx vecv)|.|vecw| is

Let veca=hati + hatj +hatk,vecb=hati- hatj + hatk and vecc= hati-hatj - hatk be three vectors. A vectors vecv in the plane of veca and vecb , whose projection on vecc is 1/sqrt3 is given by

Let vecu= hati + hatj , vecv = hati -hatj and vecw =hati + 2hatj + 3 hatk If hatn isa unit vector such that vecu .hatn=0 and vecv .hatn =0 , " then " |vecw.hatn| is equal to

Let vecu= hati + hatj , vecv = hati -hatja and hati -hatj and vecw =hati + 2hatj + 3 hatk If hatn isa unit vector such that vecu .hatn=0 and vecn .hatn =0 , " then " |vecw.hatn| is equal to

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

Let vecu=hati+hatj,vecv=hati-hatj and vecw=hati+2hatj+3hatk . If hatn is a unit vector such that vecu.hatn=0 and vecv.hatn=0, |vecw.hatn| is equal to (A) 0 (B) 1 (C) 2 (D) 3

Velocity vectors of three masses 2kg,1kg and 3 kg are vecv_1 = (hati-2hatj+hatk) m/s,vecV_2 = (2hati +2hatj -hatk) m/s and vecv_3 respectively. If velocity vector of center of mass of the system is zero then value of vecv_3 will be

Consider three vectors vecp=hati+hatj+hatk,vecq=2hati+4hatj-hatk and vecr=hati+hatj+3hatk and let vecs be a unit vector, then vecp,vecq and vecr are

If veca=hati+hatj+hatk, vecb=2hati-hatj+3hatk and vecc=hati-2hatj+hatk find a unit vector parallel to ther vector 2veca-vecb+3c .