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`.

Show that the pair of staright lines whose direction cosines are given by al+bm+cn=0 and pl^(2)+qm^(2)+rn^(2)=0 are perpendicular to each other if a^(2)(q+r)+b^(2)(r+p)+c^(2)(p+q) =0

Show that the straight lines whose direction cosines are given by 2l + 2m - n = 0 and mn + nl + Im = 0 are at right angles.

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 .

The straight lines whose direction cosines are given by al+bm+cn=0 ,fmn+gnl+hlm=0 are perpendicular if

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

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

Find the acute angle between the two straight lines whose direction cosines are given by l+m+n=0 and l^(2)+m^(2)-n^(2)=0