Show that `[vecb, vec c, vecd]veca-[veca, vec c, vecd]vecb+[veca, vecb, vecd]vec c-[veca, vecb, vec c]vecd=0`.

For any four vectors veca , vecb , vecc , vecd we have (vecaxxvecb)xx(veccxxvecd)=[veca,vecb,vecd]vecc-[veca,vecb,vecc]vecd=[veca,vecc,vecd]vecb-[vecb,vecc,vecd]veca .

If [veca+vecb, vecb+vec c, vec c+veca]=8 then [veca, vecb, vec c] is

Show that for any three vectors veca , vec b and vec c [ vec a + vec b, vecb + vec c , vec c + vec a ] =2[vec a , vec b , vecc] .

Show that (veca xx vecb) *(vecc xx vecd) +(vecb xx vecc) *(veca xx vecd) +(vecc xx veca) *(vecb xx vecd)=0 .

Show that vecaxx(vecb+vecc)+vecbxx(vecc+veca)+veccxx(veca+vecb)=vec0.

If the vectors veca, vecb, and vecc are coplanar show that |(veca,vecb,vecc),(veca.veca, veca.vecb,veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc)|=0

If veca,vecb,vecc,vecd are unit vectors such that veca.vecb=1/2 , vecc.vecd=1/2 and angle between veca xx vecb and vecc xx vecd is pi/6 then the value of |[vecavecbvecd]vecc-[vecavecbvecc]vecd|=

Statement 1: veca, vecb and vecc are three mutually perpendicular unit vectors and vecd is a vector such that veca, vecb, vecc and vecd are non- coplanar. If [vecd vecb vecc] = [vecdvecavecb] = [vecdvecc veca] = 1, " then " vecd= veca+vecb+vecc Statement 2: [vecd vecb vecc] = [vecd veca vecb] = [vecdveccveca] Rightarrow vecd is equally inclined to veca, vecb and vecc . Option A: Both the statements are true and statement 2 is the correct explanation for statement 1. Option B: Both statements are true but statement 2 is not the correct explanation for statement 1. Option C: Statement 1 is true and Statement 2 is false Option D: Statement 1 is false and Statement 2 is true.