[" Q.14.Let "vec a,vec b&vec c" be non coplanar vectors such that "],[qquad [r_(1)=a-b+c,r_(2)=b+c-a,r_(3)=a+b+c,r=2a-3b+4c],[" If "r=lambda_(1)r_(1)+lambda_(2)r_(2)+lambda_(3)r_(3)," then "]]

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

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

Let bar(a),bar(b),bar(c) are three non-coplanar vectors such that bar(r)_(1)=bar(a)-bar(b)+bar(c);bar(r)_(2)=bar(b)+bar(c)-bar(a);bar(r)_(3)=bar(c)+bar(a)+bar(b),bar(r)=2bar(a)-3bar(b)+4bar(c) .If bar(r)=lambda_(1)bar(r)_(1)+lambda_(2)bar(r)_(2)+lambda_(3)bar(r)_(3) then lambda_(1)+lambda_(2)+lambda_(3) is equal to

If vec a,vec b,vec c are non-coplanar vectors and lambda is a real number then then vectors vec a+2vec b+3vec c,lambdavec b+4vec c and (2 lambda-1)vec c are non-coplanar for

If vec(a),vec(b),vec (c ) are non - coplanar vectors vec (r) . vec(a) = vecr . vec(b) = vecr.vec(c ) = 0 , show that vec (r ) is a zero vector .

If vec r*vec a=vec r*vec b=vec r*vec c=0 where a,b,c are non-coplanar,then

Let vec a,vec b, and vec c be three non coplanar unit vectors such that the angle between every pair of them is (pi)/(3). If vec a xxvec b+vec b .If where p ,q, r are scalars then the value of (p^(2)+2q^(2)+r^(2))/(q^(2)) is