Find `[[l, m, n]]``[[a, b,c]]`

In Fig. 5.61, l, m and n are parallel lines, and the lines p and q are also parallel. Find the values of a, b and c.

|[(m+n)^(2), l^(2), mn], [(n+l)^(2), m^(2), ln], [(l+m)^(2), n^(2), lm]| =(l^(2) +m^(2) +n^(2))(l-m)(m-n)(n-l)(l+m+n)

If quad vec r=l(vec b xxvec c)+m(vec c xxvec a)+n(vec a xxvec b) and [vec a,vec b,vec c]=2, then l+m+n is equal to

Find : L.C.M. (3, 5)

If the vectors vec a, vec b, vec c are non-coplanar and l,m,n are distinct real numbers, then [(l vec a + m vec b + n vec c) (l vec b + m vec c + n vec a) (l vec c + m vec a + n vec b)] = 0, implies (A) lm+mn+nl = 0 (B) l+m+n = 0 (C) l^2 + m^2 + n^2 = 0

Let a, b, c be the side-lengths of a triangle, and l, m,n be the lengths of its medians. Put K=((l+m+n)/(a+b+c)) Then, as a, b, c vary, K can assume every value in the interval

Supose directioncoisnes of two lines are given by u l+vm+wn=0 and al^2+bm^2+cn^2=0 where u,v,w,a,b,c are arbitrary constnts and l,m,n are directioncosines of the lines. For u=v=w=1 directionc isines of both lines satisfy the relation. (A) (b+c)(n/l)^2+2b(n/l)+(a+b)=0 (B) (c+a)(l/m)^2+2c(l/m)+(b+c)=0 (C) (a+b)(m/n)^2+2a(m/n)+(c+a)=0 (D) all of the above

Give the possible value for the missing quantum number (s) in each of the following sets. (a) n=3, l=0, m_(l)=? , (b) n=3, l=?, m_(l)=-1 (c) n=?, l=1, m_(l)=+1 , (d) n=?, l=2, m_(l)=? .

If a and b vary inversely to each other, then find the values of l, m, n.