Show that :
`( vecP + vecQ ) + vecS = vecP + ( vecQ + vecS )`

if vecP +vecQ = vecP -vecQ , then

If [vec a vecb vec c] ne 0 and vecP=(vec b xx vec c)/([veca vecb vec c]), vecq=(vec c xx veca)/([veca vec b vec c]), vec r =(vec a xx vec b)/([veca vecb vec c ]) , then veca. vecp+ vecb. vecq+ vec c.vecr is equal to …………

(22) if vec p and vec q are unit vectors forming an angle of 30^@ ; find the area of the parallelogram having veca=vecp+2vecq and vecb=2vecp+vecq as its diagonals. (23) For any two vectors vec a and vec b , prove that | vec a xxvec b|^2=| [vec a* vec a ,vec a*vec b],[ vec b* vec a, vec b* vec b]| .

Let veca , vecb, vec c be three non coplanar vectors , and let vecp , vecq " and " vec r be the vectors defined by the relation vecp = (vecb xx vec c )/([veca vecb vec c ]), vec q = (vec c xx vec a)/([veca vecb vec c ]) " and " vec r = (vec a xx vec b)/([veca vecb vec c ]) Then the value of the expension (vec a + vec b) .vec p + (vecb + vec c) .q + (vec c + vec a) . vec r is equal to

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 .

The resultant of vecP and vecQ is vec R . If vecQ is doubled, vecR is doubled, when vecQ is reversed, vecR is again doubled, find P : Q : R,

If vectors vecP, vecQ and vecR have magnitudes 5,12 and 13 units and vecP + vecQ - vecR = 0 , the angle between vecQ and vecR is

If vectors vecP, vecQ and vecR have magnitudes 5, 12 and 13 units and vecP + vecQ = vecR , the angle between vecQ and vecR is :

If vecp,vecq and vecr are perpendicular to vecq + vecr , vec r + vecp and vecp + vecq respectively and if |vecp +vecq| = 6, |vecq + vecr| = 4sqrt3 and |vecr +vecp| = 4 then |vecp + vecq + vecr| is