Distance of the point `P(x_2, y_2, z_2)` from the line `(x-x_1)/l=(y-y_1)/m=(z-z_1)/n`, where `l,m,n` are the direction cosines of the line, is

The condition that the line (x-x_1)/l=(y-y_1)/m=(z-z_1)/n lies in the plane ax+by+cz+d=0 is

The condition that the line (x-x_(1))/(l)=(y-y_(1))/(m)=(z-z_(1))/(n) lies in the plane ax+by+cz+d=0 is

A line L passes through the point P(5,-6,7) and is parallel to the planes x+y+z=1 and 2x-y-2z=3. What are the direction ratios of the line of intersection of the given planes?

A line L passes through the point P(5,-6,7) and is parallel to the planes x+y+z=1 and 2x-y-2z=3 . What are the direction ratios of the line of intersection of the given planes

Find the equation of the plane through the line (x-x_1)/l_1=(y-y_1)/m_1=(z-z_1)/n_1 and parallel to the line (x-alpha)/l_2=(y-beta)/m_2=(z-gamma)/n_2

Find the equation of the plane through the line (x-x_1)/l_1=(y-y_1)/m_1=(z-z_1)/n_1 and parallel to the line (x-alpha)/l_2=(y-beta)/m_2=(z-gamma)/n_2

Find the acute angle between the lines (x-1)/(l)=(y+1)/(m)=(1)/(n) and =(x+1)/(m)=(y-3)/(n)=(z-1)/(l) where l>m>n, and l,m,n are the roots of the cubic equation x^(3)+x^(2)-4x=4

The equation of the plane containing the line (x-x_1)/l =(y-y_1)/m =(z-z_1)/n is : a(x-x_1)+b(y-y_1)+c(z-z_1)=0 , where :