If the vectors `veca, vecb, vecc, vecd` are coplanar show that `(vecaxxvecb)xx(veccxxvecd)=vec0`

If the vectors veca, vecb, vecc and vecd are coplanar vectors, then (vecaxxvecb)xx(veccxxvecd) is equal to

Let the vectors veca, vecb,vecc and vecd be such that (vecaxxvecb)xx(veccxxvecd)=vec0 . Let P_1 and P_2 be planes determined by pairs of vectors veca,vecb and vecc,vecd respectively. Then the angle between P_1 and P_2 is (A) 0 (B) pi/4 (C) pi/3 (D) pi/2

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

for any four vectors veca,vecb, vecc and vecd prove that vecd. (vecaxx(vecbxx(veccxxvecd)))=(vecb.vecd)[veca vecc vecd]

If vectors, vecb, vecc and vecd are not coplanar, the prove that vector (veca xx vecb) xx (vecc xx vecd) + ( veca xx vecc) xx (vecd xx vecb) + (veca xx vecd) xx (vecb xx vecc) is parallel to veca .

If veca,vecb,vecc and vecd are unit vectors such that (vecaxxvecb).(veccxxvecd)=1 and veca.vecc=1/2 then (A) veca,vecb,vecc are non coplanar (B) vecb,vecc, vecd are non coplanar (C) vecb, vecd are non paralel (D) veca, vecd are paralel and vecb, vecc are parallel

If veca,vecb,vecc and vecd are unit vectors such that (vecaxxvecb)*(veccxxvecd)=1 and veca.vecc=1/2, then

If the three vectors veca,vecb,vecc are non coplanar express each of vecbxxvecc, veccxxveca, vecaxxvecb in terms of veca,vecb,vecc .

If veca,vecb,vecc,vecd are any for vectors then (vecaxxvecb)xx(veccxxvecd) is a vector (A) perpendicular to veca,vecb,vecc,vecd (B) along the the line intersection of two planes, one containing veca,vecb and the other containing vecc,vecd . (C) equally inclined both vecaxxvecb and veccxxvecd (D) none of these

A, B C and D are four points in a plane with position vectors, veca, vecb vecc and vecd respectively, such that (veca-vecd).(vecb-vecc)= (vecb-vecd).(vecc-veca)=0 then point D is the ______ of triangle ABC.