यदि चार बिंदु `A(veca),B(vecb),C(vecc)` एवं `D(vecd)` समतलीय हो तो सिद्ध कीजिए कि `[vecavecbvecc]=[vecbveccvecd]+[veccvecavecd]+[vecavecbvecd]`

If veca,vecb,vecc are unity vectors such that vecd=lamdaveca+muvecb+gammavecc then gamma is equal to (A) ([veca vecb vecc])/([vecb veca vecc]) (B) ([vecb vecc vecd])/([vecb vecc veca]) (C) ([vecb vecd vecc])/([veca vecb vecc]) (D) ([vecc vecb vecd])/([veca vecb vecc])

If veca,vecb,vecc are unity vectors such that vecd=lamdaveca+muvecb+gammavecc then lambda is equal to (A) ([veca vecb vecc])/([vecb veca vecc]) (B) ([vecb vecc vecd])/([vecb vecc veca]) (C) ([vecb vecd vecc])/([veca vecb vecc]) (D) ([vecc vecb vecd])/([veca vecb vecc])

[vecaxx vecb " " vecc xx vecd " " vecexx vecf] is equal to (a) [veca vecb vecd] [vecc vece vecf]-[veca vecb vecc] [vecd vece vecf] (b) [veca vecb vece ] [vecf vecc vecd] - [veca vecb vecf] [vece vecc vecd] (c) [vecc vecd veca] [vecb vece vecf] - [veca vecd vecb] [vecavece vecf] (d) [veca vecc vece] [vecb vecd vecf]

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.

If veca, vecb and vecc be any three non coplanar vectors. Then the system of vectors veca\',vecb\' and vecc\' which satisfies veca.veca\'=vecb.vecb\'=vecc.vecc\'=1 and veca.vecb\'=veca.vecc\'=vecb.veca\'=vecb.vecc\'=vecc.veca\'=vecc.vecb\'=0 is called the reciprocal system to the vectors veca,vecb, and vecc . The value of [veca\' vecb\' vecc\']^-1 is (A) 2[veca vecb vecc] (B) [veca vecb vecc] (C) 3[veca vecb vecc] (D) 0

If veca, vecb and vecc be any three non coplanar vectors. Then the system of vectors veca\',vecb\' and vecc\' which satisfies veca.veca\'=vecb.vecb\'=vecc.vecc\'=1 veca.vecb\'=veca.veca\'=vecb.veca\'=vecb.vecc\'=vecc.veca\'=vecc.vecb\'=0 is called the reciprocal system to the vectors veca,vecb, and vecc . The value of [veca\' vecb\' vecc\']^-1 is (A) 2[veca vecb vecc] (B) [veca,vecb,vecc] (C) 3[veca vecb vecc] (D) 0

For vectors veca,vecb,vecc,vecd, vecaxx(vecbxxvecc)=(veca.vecc)vecb-(veca.vecb)vecc and (vecaxxvecb).(veccxxvecd)=(veca.vecc)(vecb.vecd)(veca.vecd)(vecb.vecc) Now answer the following question: {(vecaxxvecb).xxvecc}.vecd would be equal to (A) veca.(vecxx(veccxxvecd)) (B) ((vecaxxvecc)xxvecb).vecd (C) (vecaxxvecb).(vecdxxvecc) (D) none of these

For vectors veca,vecb,vecc,vecd, vecaxx(vecbxxvecc)=(veca.vecc)vecb-(veca.vecb)vecc and (vecaxxvecb).(veccxxvecd)=(veca.vecc)(vecb.vecd)-(veca.vecd)(vecb.vecc) Now answer the following question: {(vecaxxvecb).xxvecc}.vecd would be equal to (A) veca.(vecbxx(veccxxvecd)) (B) ((vecaxxvecc)xxvecb).vecd (C) (vecaxxvecb).(veccxxvecd) (D) none of these

For vectors veca,vecb,vecc,vecd, vecaxx(vecbxxvecc)=(veca.vecc)vecb-(veca.vecb)vecc and (vecaxxvecb).(veccxxvecd)=(veca.vecc)(vecb.vecd)(veca.vecd)(vecb.vecc) Now answer the following question: (vecaxxvecb).(vecxxvecd) is equal to (A) veca.(vecbxx(vecxxvecd)) (B) |veca|(vecb.(veccxxvecd)) (C) |vecaxxvecb|.|veccxxvecdD| (D) none of these

For vectors veca,vecb,vecc,vecd, vecaxx(vecbxxvecc)=(veca.vecc)vecb-(veca.vecb)vecc and (vecaxxvecb).(veccxxvecd)=(veca.vecc)(vecb.vecd)-(veca.vecd)(vecb.vecc) Now answer the following question: (vecaxxvecb).(veccxxvecd) is equal to (A) veca.(vecbxx(veccxxvecd)) (B) |veca|(vecb.(veccxxvecd)) (C) |vecaxxvecb|.|veccxxvecd| (D) none of these