For three vectors `vecp, vecq` and `vecr` if `vecr = 3vecp+4vecq` and `2vecr= vecp-3vecq` then

For three vectors vecP, vecQ and vecR, vecP+vecQ=vecR and P+Q=R Then prove that vecP and vecQ are parallel to each other.

Statement 1: Let veca, vecb, vecc be three coterminous edges of a parallelopiped of volume V . Let V_(1) be the volume of the parallelopiped whose three coterminous edges are the diagonals of three adjacent faces of the given parallelopiped. Then V_(1)=2V . Statement 2: For any three vectors, vecp, vecq, vecr [(vecp+vecq, vecq+vecr,vecr+vecp)]=2[(vecp,vecq,vecr)]

Statement 1: Let veca, vecb, vecc be three coterminous edges of a parallelopiped of volume V . Let V_(1) be the volume of the parallelopiped whose three coterminous edges are the diagonals of three adjacent faces of the given parallelopiped. Then V_(1)=2V . Statement 2: For any three vectors, vecp, vecq, vecr [(vecp+vecq, vecq+vecr,vecr+vecp)]=2[(vecp,vecq,vecr)]

if vecP +vecQ = vecP -vecQ , then

if vecP +vecQ = vecP -vecQ , then

Consider the vector vecp=2i-j+k . Find two vectors vecq and vecr such that vecp,vecq and vecr are mutually perpendicular.

There vectors vecP, vecQ and vecR are such that vecP+vecQ+vecR=0 Vectors vecP and vecQ are equal in , magnitude . The magnitude of vector vecR is sqrt2 times the magnitude of either vecP or vecQ . Calculate the angle between these vectors .

If three points (2 vecp-vecq+3 vecr),(vecp-2 vecq+alpha vecr) and (beta vecp-5 vecq) (where vecp, barq, vecr are non-coplanar vectors) are collinear, then the value of 1/(alpha+beta) is