If `barb` and `barc` are two non-collinear vectors, then number of solutions (x,y) in `x,yin[0,10]` satisfying the equation `baracdot[barb+barc]=5` and `baraxx(barbxxbarc)=(x^(2)-2x+7)barb+(siny)barc` is

[barb barc barbxxbarc]+{barb.barc}^(2) =

barb and barc are non collinear vectors. bara is a vector such that bara.(barb+barc)=4 and bara xx (barb xx barc)=(x^(2)-2x+6)barb+(siny) barc and 0 lt y le pi . Then the point (x, y) is

If barb, barc are like unit vectors and baraxx (barbxx barc) = bar0 then

Let bara,barb,barc be three vectors which satisfy baraxx(barbxxbarc)=(baraxxbarb)xxbarc if

If bara,barb and barc are non zero non-collinear vectors and theta(ne0,pi) is the angle between barb and barc if (baraxxbarb)xxbarc=1/3abs(barb)abs(barc)bara , then find sin theta

If barb, barc are two unit vectors along the positive x, y axes, and bara is any vector, then (bara*barb)barb+(bara*barc)barc+(bara*(barb xx barc))/(|barb xx barc|^(2))(barb xx barc)=

If bara,barb,barc are three non-coplanar vectors and barp,barq,barr are defined by the relations barp=(barbxxbarc)/(bara barb barc),barq=(barcxxbara)/(bara barb barc),barr=(baraxxbarb)/(bara barb barc) then (bara+barb).barp+(barb+barc).barq+(barc+bara).barr=

If bara,barb,barc are non-coplanar vectors, then three points with position vectors bara-2barb+3barc,2bara+mbarb-4barc and -7barb+10barc will be collinear if m equals

If bara,barb,barc are non-coplanar vectors, then three points with position vectors bara-2barb+3barc,2bara+mbarb-4barc and -7barb+10barc will be collinear if m equals