If PQRS is a quadrilteral such that `vec(PQ)=veca,vec(PS)=vecb and vec(PR)=x veca+yvecb` show that the area of the quadrilateral PQRS is `1/2|(xy||vecaxxvecb|`

ABCD is a quadrilateral with vec(AB) = veca, vec(AD) = vecb and vec(AC)=2veca+3vecb. If its area is alpha times the area of the parallelogram with AB and AD as adjacent sides, then alpha=

If ABCDEF is a regular hexagon with vec(AB) = veca and vec(BC)= vecb, then vec(CE) equals

If veca.vecb=0 and vecaxxvecb=0 prove that veca=vec0 or vecb=vec0 .

Prove that : veca*(vecb+vec c)xx(veca+2vecb+3vec c)=[veca vecb vec c]

Prove that veca*(vecb+vec c)xx (veca+3vecb+2vec c)=-(veca vecb vecc )

If vecAxxvecB=vec0 and vecBxxvecC=vec0 , then the angle between vecA and vecC may be:

In trapezium PQRS, given that QR|| PS and 2QR=PS. If vec(PQ)=veca,vec(QR)=vecb and vec(RS)=vecc , express veca in terms vecb and vecc

If vecaxxvecb=vecc,vecb xx vecc=veca, where vecc != vec0, then

If vecaxxvecb=vecc and vecbxxvecc=veca , show that veca,vecb,vecc are orthogonal in pairs. Also show that |vecc|=|veca| and |vecb|=1

If veca , vecb are unit vectors such that |vec a+vecb|=-1 " then " |2veca -3vecb| =