In Fig.56, give reasons why `l_1|(|l_2dotI s\ m_1\ |\ )|m_2?`

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

Explain giving reasons, which of the following sets of quantum numbers 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)=+1/2

If vec aa n d vec b are two non-collinear vectors, show that points l_1 vec a+m_1 vec b ,l_2 vec a+m_2 vec b and l_3 vec a+m_3 vec b are collinear if |l_1 l_2 l_3 m_1m_2m_3 1 1 1|=0.

Two lines with direction cosines l_1,m_1,n_1 and l_2,m_2,n_2 are at righat angles iff (A) l_1l_2+m_1m_2+n_1n_2=0 (B) l_1=l_2,m_1=m_2,n_1=n_2 (C) l_1/l_2=m_1/m_2=n_1/n_2 (D) l_1l_2=m_1m_2=n_1n_2

Statement I . The combined equation of l_1,l_2 is 3x^2+6xy+2y^2=0 and that of m_1,m_2 is 5x^2+18xy+2y^2=0 . If angle between l_1,m_2 is theta , then angle between l_2,m_1 is theta . Statement II . If the pairs of lines l_1l_2=0,m_1 m_2=0 are equally inclinded that angle between l_1 and m_2 = angle between l_2 and m_1 .

Statement 1: The direction cosines of one of the angular bisectors of two intersecting line having direction cosines as l_1,m_1, n_1a n dl_2, m_2, n_2 are proportional to l_1+l_2,m_1+m_2, n_1+n_2dot Statement 2: The angle between the two intersection lines having direction cosines as l_1,m_1, n_1a n dl_2, m_2, n_2 is given by costheta=l_1l_2+m_1m_2+n_1n_2dot

In Fig., if l || m|| n and /_1=60^0, find /_2.

If three mutually perpendicular lines have direction cosines (l_1,m_1,n_1),(l_2,m_2,n_2) and (l_3 ,m_3, n_3) , then the line having direction ratio l_1+l_2+l_3,m_1+ m_2+m_3, and n_1 + n_2 + n_3 , make an angle of

In Fig 66, l in e\ l m ,\ /_1=120^0\ and /_2=100^0, find out /_3\ a n d\ /_4.

The line l_1 x+ m_1 y+n=0 and l_2 x + m_2 y+n=0 will cut the coordinate axes at concyclic points if (A) l_1 m_1 = l_2 m_2 (B) l_1 m_2 = l_2 m_1 (C) l_1 l_2 = m_1 m_2 (D) l_1 l_2 m_1 m_2 = n^2