If `overlinea,overlineb,overlinec` are three non zero vectors, then `overlinea.overlineb=overlinea.overlinec=>`

If overline a,overline b,overline c are vectors of length 4, 4, 5 re-spectively, and overline a,overline b,overline c are perpendicular to overlineb +overline c,c+overlinea, overlinea + overlineb, then |overlinea+overlineb+overlinec|=

IF overlinea,overlineb,overlinec are noncoplanar, find the point of intersection of the line passing through the points 2overlinea+3overlineb-overlinec,3overlinea+4overlineb-2overlinec with the line joining the points overlinea-2overlineb+3overlinec,overlinea-6overlineb+6overlinec

Fo any four vectors overlinea,overlineb,overlinec and overlined , prove that (i) (overlineatimesoverlineb)times(overlinectimesoverlined)=[overline(ac)overlined]overlineb-[overlineboverlinecoverlined]overlinea and (ii) (overlineatimesoverlineb)times(overlinectimesoverlined)=[overlineaoverline(bd)]overlinec-[overlineaoverlineboverlinec]overlined

IF overlinea=2overlinei-overlinek,overlineb=-overlinei+2overlinej-4overlinek,overlinec=overlinei+overlinej+overlinek then find (overlineatimesoverlineb).(overlinebtimesoverlinec)

IF overlinea,overlineb,overlinec are non-coplanar, then prove that the points with position vectors 2overlinea+3overlineb-overlinec,overlinea-2overlineb+3overlinec,3overlinea+4overlineb-2overlinec,overlinea-6overlineb+6overlinec are coplanar.

Show that the four points -overlinea+4overlineb-3overlinec,3overlinea+2overlineb-5overlinec,-3overlinea+8overlineb-5overlinec,-3overlinea+2overlineb+overlinec are coplanar, where overlinea,overlineb,overlinec are non-coplanar vectors.

IF overlinea=overlinei+2overlinej-3overlinek and overlineb=3overlinei-overlinej+2overlinek then show that overlinea+overlineb and overlinea-overlineb are perpendicular to each other.

Let overlinea=2overlinei+4overlinej-5overlinek,overlineb=overlinei+overlinej+overlinek,overlinec=overlinej+2overlinek . Find the unit vector in the opposite direction of overlinea+overlineb+overlinec

Let overlinea=2overlinei+4overlinej-5overlinek,overlineb=overlinei+overlinej+overlinek,overlinec=overlinej+2overlinek . Find the unit vector in the opposite direction of overlinea+overlineb+overlinec