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STATEMENT-1 : If veca and vecb be two gi...

STATEMENT-1 : If `veca` and `vecb` be two given non zero vectors then any vector `vecr` coplanar with `veca` and `vecb` can be represented as `vecr=xveca+yvecb` where x &yare some scalars.
STATEMENT-2 : If `veca,vecbvecc` are three non-coplanar vectors, then any vector `vecr` in space can be expressed as `vecr=xveca+yvecb+zvecc`, where x,y,z are some scalars.
STATEMENT-3 : If vectors `veca & vecb` represent two sides of a triangle, then `lambda(veca+vecb)` (where `lambda ne 1`) can represent the vector along third side.

A

F T T

B

T T F

C

F T F

D

T T T

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Knowledge Check

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

    A
    `vecaxxvecb+vecbxxvecc+veccxxveca`
    B
    `1/([(veca, vecb, vecc)]){vecaxxvecb+vecbxxvec+veccxxveca}`
    C
    `[(veca, vecb, vecc)]{vecaxxvecb+vecbxxvecc+vecxxveca}`
    D
    none of these

  • If veca and vecb are othogonal unit vectors, then for a vector vecr non - coplanar with veca and vecb vector vecr xx veca is equal to

    A
    `[vecr vecavecb]vecb - (vecr.vecb)(vecbxxveca)`
    B
    `[vecrvecavecb] (veca+vecb)`
    C
    `[vecr vecavecb]veca + (vecr.veca) vecaxxvecb`
    D
    none of these

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

    A
    straight line
    B
    plane
    C
    plane pasing through the origin
    D
    sphere

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