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 .

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

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

The straight lines,whose direction cosines are l,m,n which are the roots of al+bm+cn=0 and fl^(2)+gm^(2)+hn^(2)=0 are parallel

The direction cosines of two lines are related by l+m+n=0 and al^(2)+bm^(2)+cn^(2)=0 The linesare parallel if

If the direction cosines of two lines given by the equations p m+qn+rl=0 and lm+mn+nl=0 , prove that the lines are parallel if p^2+q^2+r^2=2(pq+qr+rp) and perpendicular if pq+qr+rp=0

The direction ratios of two lines satisfy the relation 2a - b + 2c = 0 and ab + bc + ca = 0 . Show that the lines are perpendicular.

IF the direction ratios of two vectors are connected by the relations p + q + r = 0 and p^(2) + q^(2) - r^(2) = 0. Find the angle between them.

The equations of the tangents drawn from the origin to the circle x^2 + y^2 - 2px - 2qy + q^2 = 0 are perpendicular if (A) p^2 = q^2 (B) p^2 = q^2 =1 (C) p = q/2 (D) q= p/2