Prove that the two lines whose direction cosines are given by the relations `pl+qm+rn=0 and al^2+bm^2+cn^2=0` are perpendicular if `p^2(b+c)+q^2(c+a)+r^2(a+b)=0` and parallel if `p^2/a+q^2/b+r^2/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 al+bm+cn=0, fmn+gnl+hlm=0 are: perpendicular if f/a+g/b+h/c=0

Show that the straight lines whose direction cosines are given by al+bm+cn=0 and pl^(2)+qm^(2)+rn^(2)=0 are parallel if a^(2)/p+b^(2)/q+c^(2)/r=0 .

Prove that the straight lines whose direction cosines are given by a^(2)l+b^(2)m+c^(2)n=0 and mn+nl+lm=0 are parallel if a+b+c=0 .

Show that the straight lines whose direction cosines are given by the equations al+bm+cn=0 and u l^2+v m^2+w n^2=0 are parallel or perpendicular as a^2/u+b^2/v+c^2/w=0 or a^2(v +w)+b^2(w+u)+c^2(u+v)=0

Show that the straight lines whose direction cosines are given by the equations al+bm+cn=0 and u l^2+v m^2+w n^2=0 are parallel or perpendicular as a^2/u+b^2/v+c^2/w=0 or a^2(v +w)+b^2(w+u)+c^2(u+v)=0

Show that the straight lines whose direction cosines are given by the equations al+bm+cn=0 and u l^2+z m^2=v n^2+w n^2=0 are parallel or perpendicular as a^2/u+b^2/v+c^2/w=0 or a^2(v +w)+b^2(w+u)+c^2(u+v)=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

Show that the straight lines whose direction cosines are given by the equations al+bm+cn=0 and ul^(2)+zm^(2)=vm^(2)+wn^(2)=0 are parallel or perpendicular as (a^(2))/(u)+(b^(2))/(v)+(c^(2))/(w)=0 or a^(2)(v+w)+b^(2)(w+u)+c^(2)(u+v)=0