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Show that veca, vecb and vec c are copla...

Show that `veca, vecb and vec c` are coplanar`if veca+vecb,vecb+vecc and vecc+veca ` are coplanar.

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Explore conceptually related problems

Prove that veca xx (vecb xx vecc) + vecb xx (vecc xx veca) + vecc xx (veca xx vecb) = vec0 and hence prove that veca xx (vecb xx vecc), vecb xx (vecc xx veca), vecc xx (veca xx vecb) are coplanar.

Prove that the four points with position vectors 2veca+3vecb-vecc, veca-2vecb+3vecc, 3veca+4vecb-2vecc and veca-6vecb+6vecc are coplanar.

Knowledge Check

  • If veca , vecb and vecc are non-zero vectors, then vecaxxvecb = vecaxxvecc

    A
    `vecb` = `vecc`
    B
    `veca||(vecb-vecc)
    C
    `vecb||vecc`
    D
    `vecbbotvecc`

  • If veca.vecb = vecc.veca for all vectors veca , then

    A
    `vecabot(vecb-vecc)`
    B
    `vecb-vecc` = 0
    C
    `vecbnevecc`
    D
    `vecb+vecc` = 0

  • If vecA xx vecB=vecC then

    A
    C is prependicular`vecA` only
    B
    `vecC` is parallel to` vecA`
    C
    C is prependicular to both` vecA` and `vecB`
    D
    C is parallel to`vecA` and `vecB`

    • Similar Questions

    Explore conceptually related problems

    If veca,vecb and vecc are three vectors such that veca x vecb = vecc and vecb x vecc = veca , then prove that veca,vecb and vecc are mutually at right angles and |vecb| = 1,|vecc| = |veca|

    If veca,vecb,vecc are such that veca.vecb = veca.vecc then show that veca = vec0 or vecb = vecc or veca is perpendicular to vecb.vecc .

    Three vectors veca, vecb and vecc satisfy the condition veca + vecb + vecc = 0 . Find the value of veca.vecb + vecb.vecc + vecc.veca if |veca| = 1, |vecb|= 4, |vecc|= 2 .

    |veca| = |vecb| = veca = vecb .

    If veca,vecb and vecc are three vectors such that |veca|=5,|vecb|=12,|vecc|=13 and veca+vecb+vecc=0 then find the value of veca.vecb+vecb.vecc+vecc.veca.

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