Home
Class 12
MATHS
If veca, vecb, vecc are three non-coplan...

If `veca, vecb, vecc` are three non-coplanar vectors, then a vector `vecr` satisfying `vecr.veca=vecr.vecb=vecr.vecc=1`, is

A

`veca + 2vecb + 3vecc`

B

`vecb xx vecc + 2vecc xx veca + 3veca xx vecb`

C

`(vecb.vecc)veca+2(vecc.veca)vecb+3(veca.vecb)vecc`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Similar Questions

Explore conceptually related problems

If veca,vecb and vecc are three non-coplanar vectors, then the vector equation vecr-(1-p-q)veca+pvecb+qvecc represents a

If vecp=(vecbxxvecc)/([(veca,vecb,vecc)]),vecq=(veccxxveca)/([(veca,vecb,vecc)]),vecr=(vecaxxvecb)/([(veca,vecb,vecb)]) where veca,vecb,vecc are three non-coplanar vectors, then the value of the expression (veca+vecb+vecc).(vecp+vecq+vecr) is

If veca, vecb, vecc are any three non coplanar vectors, then (veca+vecb+vecc).(vecb+vecc)xx(vecc+veca)

Statement 1: Let vecr be any vector in space. Then, vecr=(vecr.hati)hati+(vecr.hatj)hatj+(vecr.hatk)hatk Statement 2: If veca, vecb, vecc are three non-coplanar vectors and vecr is any vector in space then vecr={([(vecr, vecb, vecc)])/([(veca, vecb, vecc)])}veca+{([(vecr, vecc, veca)])/([(veca, vecb, vecc)])}vecb+{([(vecr, veca, vecb)])/([(veca, vecb, vecc)])}vecc

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

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

If veca,vecb,vecc are three non coplanar vectors then the vector equation vecr=(1-p-q)veca+pvecb+qvecc are represents a: (A) straighat line (B) plane (C) plane passing through the origin (D) sphere

Statement 1: Any vector in space can be uniquely written as the linear combination of three non-coplanar vectors. Stetement 2: If veca, vecb, vecc are three non-coplanar vectors and vecr is any vector in space then [(veca,vecb, vecc)]vecc+[(vecb, vecc, vecr)]veca+[(vecc, veca, vecr)]vecb=[(veca, vecb, vecc)]vecr

If veca, vecb, vecc are any three non coplanar vectors, then [(veca+vecb+vecc, veca-vecc, veca-vecb)] is equal to

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