`|[(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)`

Factoris the expression. l ^(2) m ^(2) n - lm ^(2) n ^(2) - l^(2) mn ^(2)

Write the greatest common factor in each of the term. l ^(2) m ^(2) n, l m ^(2) n ^(2) , l ^(2) mn ^(2)

If l, m and n are real numbers such that l^(2)+m^(2)+n^(2)=0 , then |(1+l^(2),lm,l n),(lm,1+m^(2),mn),(l n,mn,1+n^(2))| is equal to a)0 b)1 c) l+m+n+2 d) 2(l+m+n)+3

Add the following: l^2 + m^2, m^2 + n^2, n^2 + l^2, 2lm + 2mn + 2nl

Show that the matris [[l_(1),m_(1),n_(1)],[l_(2),m_(2),n_(2)],[l_(3),m_(3),n_(3)]] is orthogonal, if l_(1)^(2) + m_(1)^(2) + n_(1)^(2) = Sigmal_(1)^(2) = 1 = Sigma l_(2)^(2) = Sigma_(3) ^(2) and l_(1) l_(2) + m_(1)m_(2) + n_(1) n_(2) = Sigma l_(1)l_(2) =0 = Sigma l_(2)l_(3) = Sigma l_(3) l_(1).

Simply (x^(m)/x^(n))^(m^(2)+mn+n^(2))xx(x^(n)/x^(l))^(n^(2)+nl+l^(2))xx(x^(l)/x^(m))^(l^(2)+lm+m^(2))

Given sin alpha+sin beta=l,cos alpha+cos beta=mtan((alpha)/(2))tan((beta)/(2))=n,(A)(l^(2)+m^(2))(1-n)=2l(1+n)(B)(l^(2)+m^(2))(1+n)=2l(1-n)(C)(l^(2)+m^(2))(1-n)=2m(1+n)(D)(l^(2)+m^(2))(1+n)=2m(1-n)

Explain giving reasons which of the following sets of quantum number are not possible (a ) n=0, l =0 m_(l) = 0, m_(s ) =+ (1)/(2) ( b) n=1 , l = 0 m_(l) = 0, m_(s ) = - (1)/(2) ( c) n=1 , l = 1, m_(l ) = 0, m_(s ) = + (1)/(2) (d ) n= 2, l = 1, m_(l ) = 0, m_(s ) = (1) /(2) ( e) n=3, l = 3, m_(l) = 3, m_(s ) = + (1)/(2) (f ) n=3, l = 1, m_(l) = 0, m_(s) l = + (1)/(2)