`8l^3-36 l^2m+54 l m^2-27 m^3`

If 8l^2+35 m^2+36 l m+6l+12 m+1=0 and the line l x+m y+1=0 touches a fixed circle whose centre is (alpha,beta) and radius is ' r^(prime), then the value of (alpha+beta-r) is equal to

Factories the following : l^(3) - 8m^(3) - 27m^(3) - 18lmn

If cosec θ – sin θ = l and sec θ – cos θ = m, then l2 m2 (l2 + m2 + 3) =?

Subtract : 3l(l - 4m + 5n) from 4l(10n - 3m + 2l)

Prove that the three lines from O with direction cosines l_1, m_1, n_1: l_2, m_2, n_2: l_3, m_3, n_3 are coplanar, if l_1(m_2n_3-n_2m_3)+m_1(n_2l_3-l_2n_3)+n_1(l_2m_3-l_3m_2)=0

Prove that the three lines from O with direction cosines l_1, m_1, n_1: l_2, m_2, n_2: l_3, m_3, n_3 are coplanar, if l_1(m_2n_3-n_2m_3)+m_1(n_2l_3-l_2n_3)+n_1(l_2m_3-l_3m_2)=0

Prove that the three lines from O with direction cosines l_1, m_1, n_1: l_2, m_2, n_2: l_3, m_3, n_3 are coplanar, if l_1(m_2n_3-n_2m_3)+m_1(n_2l_3-l_2n_3)+n_1(l_2m_3-l_3m_2)=0

Prove that the three lines from O with direction cosines l_1, m_1, n_1: l_2, m_2, n_2: l_3, m_3, n_3 are coplanar, if l_1(m_2n_3-n_2m_3)+m_1(n_2l_3-l_2n_3)+n_1(l_2m_3-l_3m_2)=0