If `vec a,vec b,vec c` are three vectors with magnitudes `2,3` and `1` respectively and `vec a*vec c=(1)/(4)`. If the following relation holds true for some `lambda(!=0),vec b-lambdavec a=3vec c` then the value of `lambda` is

Let vec a,vec b and vec c be three vectors having magnitudes 1,5 and 3, respectively,such that the angel between vec a and vec b is theta and vec a xx(vec a xxvec b)=c. Then tan theta is equal to a 0 b.2/3 c.3/5 d.3/4

If vec a,vec b,vec c are the position vectors of points A,B,C and D respectively such that (vec a-vec d)*(vec b-vec c)=(vec b-vec d)*(vec c-vec a)=0 then D is the

If vec(a),vec(b),vec(c) are mutually perpendicular vectors having magnitudes 1,2,3 respectively, then [vec(a)+vec(b)+vec(c)" "vec(b)-vec(a)vec(c)]=

If three vector 2vec i-vec j-vec k,vec i+2vec j-3vec k,3vec i+lambdavec j+5vec k are coplanar then the value of lambda is :

If vec a,vec b,vec c are three vectors such that their magnitude is sqrt(3),1,2 and vec a xx(vec a xxvec c)+3vec b=vec 0 and theta is the angle between vec a and vec c then find the value of cos^(2)theta

If vec a,vec b,vec c are three vectors such that vec a+vec b+vec c=vec 0 and |vec a|=3,|b|=4,|vec c|=5 Find the value of vec a*vec b+vec b*vec c+vec c*vec a

If vec a,vec b and vec c are three non-zero vectors,prove that [vec a+vec b,vec b+vec c,vec c+vec a]=2[vec a,vec b,vec c]

Let vec a,vec b and vec c are vectors of magnitude 3,4,5 respectively.If vec a is perpendicular to vec b+vec c,vec b is perpendicular to vec c+vec a and vec c is perpendicular to vec a+vec b then find the magnitude of vec a+vec b+vec c

vec a,vec b,vec c are three vectors of which every pair is non-collinear.If the vectors vec a+2vec b and vec b+3vec c are collinear with vec c and vec a respectively then vec a+2vec b+6vec c is

If vec a,vec b,vec c and vec d are the position vectors of the points A,B,C and D respectively in three dimensionalspace no three of A,B,C,D are collinear and satisfy the relation 3vec a-2vec b+vec c-2vec d=0, then