Home
Class 12
MATHS
If veca,vecb,vecc are coplanar vectors ,...

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`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    FIITJEE|Exercise SOLVED PROBLEMS (OBJECTIVE)|27 Videos

  • DETERMINANT

    FIITJEE|Exercise EXERCIESE 1|3 Videos

  • DETERMINANT

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

  • DEFINITE INTEGRAL

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

  • ELLIPSE

    FIITJEE|Exercise NUMERICAL BASED|4 Videos

Similar Questions

Explore conceptually related problems

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+2vecb+3vecc)xx(vecb+2vecc+3veca)],.(vecc+2veca+3vecb)]=54 where veca,vecb and vecc are 3 non - coplanar vectors, then the values of |{:(veca.veca,veca.vecb,veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc),(vecc.veca,vecc.vecb,vecc.vecc):}| is equal to

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

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

If veca,vecb,vecc are coplanar, show that veca+vecb, vecb+vecc, vecc+veca are also coplanar.

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 any three vectors such that (veca+vecb).vecc=(veca-vecb)=vecc=0 then (vecaxxvecb)xxvecc is

Statement 1: If V is the volume of a parallelopiped having three coterminous edges as veca, vecb , and vecc , then the volume of the parallelopiped having three coterminous edges as vec(alpha)=(veca.veca)veca+(veca.vecb)vecb+(veca.vecc)vecc vec(beta)=(veca.vecb)veca+(vecb.vecb)vecb+(vecb.vecc)vecc vec(gamma)=(veca.vecc)veca+(vecb.vecc)vecb+(vecc.vecc)vecc is V^(3) Statement 2: For any three vectors veca, vecb, vecc |(veca.veca, veca.vecb, veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc),(vecc.veca,vecc.vecb,vecc.vecc)|=[(veca,vecb, vecc)]^(3)

If veca, vecb, vecc are non-coplanar vectors, then (veca.(vecb xx vecc))/(vecb.(vecc xx veca)) + (vecb.(vecc xx veca))/(vecc.(veca xx vecb)) +(vecc.(vecb xx veca))/(veca. (vecb xx vecc)) is equal to: