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 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.

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 a l+b m+c n=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=0ora^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 a l+b m+c n=0 and u l^2+vm^2+wn^2=0 are parallel or perpendicular as (a^2)/u+(b^2)/v+(c^2)/w=0ora^2(v+w)+b^2(w+u)+c^2(u+v)=0.

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 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

Prove that 2/(b+c)+2/(c+a)+2/(a+b) >0.

If the ratio of the roots of the equation x^2+p x+q=0 are equal to ratio of the roots of the equation x^2+b x+c=0 , then prove that p^2c=b^2qdot

If the ratio of the roots of the equation x^2+p x+q=0 are equal to ratio of the roots of the equation x^2+b x+c=0 , then prove that p^(2)c=b^2qdot