Evaluate :
`( veca + vec b ).( veca + vec b )`

It is given that : vec x = (vec b xx vec c)/([veca vec b vec c]) ; vecy=(vec c vec a)/([veca vecb vecc]) ; vecz=(veca xx vecb)/([veca vecb vecc]) where a, b, c are non-coplanar vectors; show that x, y, z also form a non-coplanar system. Find the value of vecx*(veca+vecb)+vecy*(vecb+vecc)+vecz(vecc+veca) .

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

If the points P( veca + 2 vec b + vec c ), Q (2 veca + 3 vecb), R (vecb+ t vec c ) are collinear, where veca , vec b , vec c are non-coplanar vectors, the value of t is

Let vec a , vec b ,vec c are three non- coplanar vectors such that vecr_(1)=veca + vec c , vecr_(2)= vec b+vec c -veca , vec r_(3) = vec c + vec a + vecb, vec r = 2 vec a - 3 vec b + 4 vec c. If vec r = lambda_(1)vecr_(1)+lambda_(2)vecr_(2)+lambda_(3)vecr_(3) , then

If veca = hati +hatj , vecb = 2hatj - hatk " and " vecr xx veca = vecb xx vec a , vecr xx vec b = veca xx vec b , then what is the value of (vec r)/(|vec r|)

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 …………

If the vectors vec a, b, c are coplanar, then the value of |(veca, vecb, vecc), (veca.a, veca.b, veca.c), (vecb.a, vecb.b, vecb.c)|

veca , vec b , vec c are non-coplanar vectors and x vec a + y vec b + z vec c = vec 0 then

Let vec r xx veca = vec b xx veca and vecc vecr=0 , where veca.vecc ne 0 , then veca.vecc(vecr xx vecb)+(vecb.vecc)(veca xx vecr) is equal to __________.

Let | vec A _ 1 | = 3 , | vec A _ 2 | = 5 and | vecA _ 1 + vecA _ 2 | = 5 . The value of ( 2 vec A _ 1 + 3 vecA _ 2 ). (3 vecA _ 1 - 2 vecA _ 2 ) is ____________.