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

If veca,vecb,vecc are non-coplanar vectors and vecu and vecv are any two vectors. Prove that vecuxxvecv=(1)/([vecavecbvecc])|{:(vecu.veca,vecv.veca,veca),(vecu.vecb,vecv.vecb,vecb),(vecu.vecc,vecv.vecc,vecc):}|

If u and v are two non-collinear unit vectors such that |vecu × vecv| = ∣ ​ (vecu − vecv) /2 ​ ∣ ​ , then the value of ∣ vecu ×( vecu × vecv) ∣ ^2 is equal to

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 .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 .vecu is (a) 47 (b) -25 (c) 0 (d) 25

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 .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

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]=

If vecu,vecv and vecw are three non coplanar vectors then (vecu+vecv-vecw).(vecu-vecv)xx(vecv-vecw) equals (A) vecu.(vecvxxvecw) (B) vecu.vecwxxvecv (C) 2vecu.(vecvxxvecw) (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 .

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