Home
Class 12
MATHS
If veca,vecb,vecc are non-coplanar vecto...

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):}|`

Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    AAKASH INSTITUTE|Exercise SECTION-I (Subjective Type Questions)|5 Videos
  • TRIGNOMETRIC FUNCTIONS

    AAKASH INSTITUTE|Exercise Section - J (Akash Challengers Question)|15 Videos

Similar Questions

Explore conceptually related problems

Show that [veca vecb vecc]\^2=|(veca.veca,veca.vecb,veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc),(vecc.veca,vecc.vecb,vecc.vecc)|

If veca, vecb, vecc are three given non-coplanar vectors and any arbitrary vector vecr in space, where Delta_(1)=|{:(vecr.veca,vecb.veca,vecc.veca),(vecr.vecb,vecb.vecb,vecc.vecb),(vecr.vecc,vecb.vecc,vecc.vecc):}|,Delta_(2)=|{:(veca.veca,vecr.veca,vecc.veca),(veca.vecb,vecr.vecb,vecc.vecb),(veca.vecc,vecr.vec ,vecc.vecc):}| Delta_(3)=|{:(veca.veca,vecb.veca,vecr.veca),(veca.vecb,vecb.vecb,vecr.vecb),(veca.vecc,vecb.vecc,vecr.vecc):}|'Delta=|{:(veca.veca,vecb.veca,vecc.veca),(veca.vecb,vecb.vecb,vecc.vecb),(veca.vecc,vecb.vecc,vecc.vecc):}|, "then prove that " vecr=(Delta_(1))/Deltaveca+(Delta_(2))/Deltavecb+(Delta_(3))/Deltavecc

veca , vecb and vecc are three non-coplanar vectors and vecr . Is any arbitrary vector. Prove that [vecbvecc vecr]veca+[vecc veca vecr]vecb+[vecavecbvecr]vecc=[veca vecb vecc]vecr .

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 vector veca,vecb,vecc are coplanar show that |(veca,vecb,vecc),(veca.veca,veca.vecb,veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc)|

If veca,vecb,vecc are coplanar vectors , then show that |{:(veca,vecb,vecc),(veca*veca,veca*vecb,veca*vecc),(vecb*veca,vecb*vecb,vecb*vecc):}|=vec0

Let veca,vecb and vecc be a set of non- coplanar vectors and veca'veab' and vecc' be its reciprocal set. prove that veca=(b'xxc')/([veca'vecb'vecc']),vecb=(c'xxa')/([veca'vecb'vecc'])andvecc=(a'xxb')/([veca'vecb'vecc'])

Let veca,vecb and vecc be a set of non- coplanar vectors and veca'veab' and vecc' be its reciprocal set. prove that veca=(b'xxc')/([veca'vecb'vecc']),vecb=(c'xxa')/([veca'vecb'vecc'])andvecc=(a'xxb')/([veca'vecb'vecc'])

If veca, vecb, vecc are non-null non coplanar vectors, then [(veca-2vecb+vecc, vecb-2vecc+veca, vecc-2veca+vecb)]=

If veca, vecb and vecc 1 are three non-coplanar vectors, then (veca + vecb + vecc). [(veca + vecb) xx (veca + vecc)] equals