[" Prove that the lines whose direction cosines are given by the relation "],[a ell+bm+cn=0" and "fmn+gn ell+h ell m=0" are perpendicular if "(f)/(a)+(g)/(b)+(h)/(c)=0]

Prove that the straight lines whose direction cosines are given by the relations al+bm+cn=0 and fmn+gnl+hlm=0 are Perpendicular to each other if (f)/(a)+(g)/(b)+(h)/(c)=0 , and parallel if a^(2)f^(2)+b^(2)g^(2)+c^(2)h^(2)-2bcgh-2cahf-2abfg=0 .

Prove that the straight lines whose direction cosines are given by the relations a l+b m+c n=0a n dfm n+gn l+hl m=0 are perpendicular, if f/a+g/b+h/c=0 and parallel, if a^2f^2+b^2g^2+c^2h^2-2a bfg-2b cgh-2a c hf=0.

Prove that the lines whose direction cosines are given by the equations l+m+n=0 and 3lm-5mn+2nl=0 are mutually perpendicular.

Prove that the lines whose direction cosines are given by the equations l+m+n=0 and 3lm-5mn+2nl=0 are mutually perpendicular.

Prove that the straight lines whose direction cosines are given by the equations al+bm+cn=0 and fmn+gnl+hlm=0 are at right angles if f/a+g/b+h/c=0

Prove that the straight lines whose direction cosines are given by the equations al+bm+cn=0 and fmn+gnl+hlm=0 are parallel if a^(2)f^(2)+b^(2)g^(2)+c^(2)h^(2)-2(abfg+bcgh+cahf)=0

Find the angle between the lines whose direction cosines are given by the equations: 2l-m+2n=0 mn+nl+lm=0.