[" Question: "42" (single Choice Type) "],[" The given figure represents a material which is "],[rArrvec rArr rarr(3)/(3)],[vec vec lambda]

Let vec a be a unit vector and vec b a non-zero vector not parallel to vec a The angles of the triangle, two of whose sides are represented by sqrt(3)(vec a xxvec b) and (vec b-(vec a*vec b)vec a are

If vec a and vec b are non-collinear vectors,then the value of x for which vectors rarrvec alpha=(x-2)vec a+vec b and vec beta=(3+2x)vec a-2vec b are collinear,is given by (i) (1)/(2)(iii)(1)/(4)(iii)0(iv)-1

7.Let vec a,vec b and vec c be three unit vectors such that vec a+vec b+vec c=vec 0 .If lambda=vec a*vec b+vec b*vec c+vec c*vec a , vec d=vec a timesvec b+vec b timesvec c+vec c timesvec a ,then the ordered pair (lambda,vec d) is equal to , 1) (-(3)/(2),3vec c timesvec b) 2) ((3)/(2),3vec a timesvec c) 3) (-(3)/(2),3vec a timesvec b) 4) ((3)/(2),3vec b timesvec c)

Let vec a,vec b,vec c be vectors represented by co-terminous edge of tetrahedron such that vec a^(^^)vec b=vec b^(^^)vec c=vec c^(^^)vec a=(pi)/(3) and |vec a|=sqrt(2);|vec b|=2,|vec c|=3 .The volume of tetrahedron is

Determine lambda such that a vector vec(r) is at right angles to each of the vectors vec(a) = lambda hat(i) + hat(j) + 3hat(k), vec(b) = 2hat(i) + hat(j) - lambda hat(k), vec(c) = -2hat(i) + lambda hat(j) + 3hat(k) .

Two vectors vec P and vec Q of the same type with tails at a point O are inclined at angle theta . The diagonal of the parallelogram, drawn with vec P and vec Q as adjacent sides, represents their resultant. Then the area of the parallelogram is given by

If D,E and F are the mid-points of the sides BC, CA and AB respectively of a triangle ABC and lambda is scalar, such that vec(AD) + 2/3vec(BE)+1/3vec(CF)=lambdavec(AC) , then lambda is equal to

If D,E and F are the mid-points of the sides BC, CA and AB respectively of a triangle ABC and lambda is scalar, such that vec(AD) + 2/3vec(BE)+1/3vec(CF)=lambdavec(AC) , then lambda is equal to

If D,E and F are the mid-points of the sides BC, CA and AB respectively of a triangle ABC and lambda is scalar, such that vec(AD) + 2/3vec(BE)+1/3vec(CF)=lambdavec(AC) , then lambda is equal to

The magnitudes of vectors vec OA,vec OB and vec OC( in figure( 2-W3) are equal.Find the direction of )/(Ovec A)+vec OB-vec OC.