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

For any two vectors vecu and vecv , prove that (i) |vecu.vecv|^(2) + |vecu xx vecv|^(2) = |vecu|^(2)|vecv|^(2) and (ii) (1+|vecu|^(2))(1+|v|^(2)) =|1-vecv+(vecu xx vecv)|^(2)

If vecu, vecv, and vecw are three non-caplanar vectors, then prove that (vecu+vecv-vecw).(vecu-vecv)xx(vecv-vecw)=vecu.vecvxxvecw

If vecu, vecv, vecw are three vectors such that [vecu vecv vecw]=1 , then 3[vecu vecv vecw]-[vecv vecw vecu]-2[vecw vecv vecu]=

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 vectors such that vecu+ vecv + vecw =0 if |vecu|= 3, |vecv|=4 and |vecw|=5 then vecu.vecv + vecv .vecw + vecw + vecw .vecu is

Let vecu,vecv and vecw be vectors such that vecu+ vecv + vecw =0 if |vecu|= 3, |vecv|=4 and |vecw|=5 then vecu.vecv + vecv .vecw + vecw + vecw .vecu is

If veca and vecb are two non collinear vectors and vecu=veca-(veca.vecb)vecb and vecv=vecaxxvecb then |vecv| is (A) |vecu| (B) |vecu|+|vecu.vecb| (C) |vecu|+|vecu.veca| (D) none of these

If vecu,vecv and vecw are three non coplanar vectors then (vecu+vecv-vecw).(vecu-vecc)xx(vecv-vecw) equals (A) vecu.vecvxxvecw (B) vecu.vecwxxvecv (C) 3vecu.vecuxxvecw (D) 0

Let vecu and vecv be unit vectors. If vecw is a vector such that vecw+vecwxxvecu=vecv , then prove that |(vecuxxvecv).vecw|le1/2 and that the equality holds if and only if vecu is perpendicular to vecv .