find three- dimensional vectors, `vecv1, vecv2 and vecv3 " satisfying " vecv_(1) .vecv_(2) = -2, vecv_(1). Vecv_(3) = 6 , vecv_(2) , vecv_(2) = 2 vecv_(2) . Vecv_(3) = -5, vecv_(3) .vecv_(3) = 29`

Let veca vecb and vecc be non- zero vectors aned vecV_(1) =veca xx (vecb xx vecc) and vecV_(2) = (veca xx vecb) xx vecc .vectors vecV_(1) and vecV_(2) are equal . Then

find 3- dimensional vectors overset(to)(v)_(1) , overset(to)(v)_(2), overset(to)(v)_(3) satisfying overset(to)(v)_(1).overset(to)(v)_(1) =4, overset(to)(v)_(1).overset(to)(v)_(2)=-2overset(to)(v)_(1).overset(to)(v)_(3)-6 overset(to)(v)_(2).overset(to)(v)_(2)=2,overset(to)(v)_(2).overset(to)(v)_(3) =-5 , overset(to)(v)_(3).overset(to)(v)_(3)=29

Let vecu, vecv and vecw be three unit vectors such that vecu + vecv + vecw = veca, vecuxx (vecv xx vecw)= vecb, (vecu xx vecv) xx vecw= vecc, vec a.vecu=3//2, veca.vecv=7//4 and |veca|=2 Vector vecu is

Let vecu, vecv and vecw be three unit vectors such that vecu + vecv + vecw = veca, vecuxx (vecv xx vecw)= vecb, (vecu xx vecv) xx vecw= vecc, vec a.vecu=3//2, veca.vecv=7//4 and |veca|=2 Vector vecu is

For any two vectors vecu and vecv prove that (1+|vecu|^2(1+|vecv|^20=(1-vecu.vecc)^2+|vecu+vecv+vecuxxvec|^2

If the vectors veca and vecb are perpendicular to each other then a vector vecv in terms of veca and vecb satisfying the equations vecv.veca=0, vecv.vecb=1 and [(vecv. vecaxx vecb)]=1 is

If vecV=2vec i+ vec(j) - vec(k) " and " vec(W) = vec(i) + 3vec(k) . if vec (U) is a unit vectors then the maximum value of the scalar triple product [vec(U) , vec(V) , vec(W)] is

vecu, vecv and vecw are three nono-coplanar unit vectors and alpha, beta and gamma are the angles between vecu and vecu, vecv and vecw and vecw and vecu , respectively and vecx , vecy and vecz are unit vectors along the bisectors of the angles alpha, beta and gamma. respectively, prove that [vecx xx vecy vecy xx vecz vecz xx vecx) = 1/16 [ vecu vecv vecw]^(2) sec^(2) alpha/2 sec^(2) beta/2 sec^(2) gamma/2 .

Let vecu, vecv and vecw be vector such that vecu+vecv+vecw=vec0 . If |vecu|=3, |vecv|=4 and |vecw|=5 then vecu.vecv+vecv.vecw+vecw.vecu is ………………….. .

Let veca and vecb be two non-collinear unit vectors. If vecu=veca-(veca.vecb)vecb and vecv=vecaxxvecb , then |vecv| is