Show that if the axes are rectangular the equation of line through point `(x_1,y_1,z_1)` at right angle to the lines `x/l_1=y/m_1=z/n_1,x/l_2=y/m_2=z/n_2` is `(x-x_1)/(m_1n_2-m_2n_1)=(y-y_1)/(n_1l_2-n_2l_1)=(z-z_1)/(l_1m_2-l_2m_1)`

Show that, if the axes are rectangular, the equations of the line through (x_1, y_1, z_1) at right angles to the lines: x/l_1=y/m_1=z/n_1,x/l_2=y/m_2=z/n_2 are frac{x-x_1}{m_1n_2-m_2n_1}=frac{y-y_1}{n_1l_2-n_2l_1}=frac{z-z_1}{l_1m_2-l_2m_1}

Show that if the axes are rectangular,the equation of the line through the point (x_(1),y_(1),z_(1)) at right angle to the lines (x)/(l_(1))=(y)/(m_(1))=(z)/(n_(1));(x)/(l_(2))=(y)/(m_(2))=(z)/(n_(2)) is (x-x_(1))/(m_(1)n_(2)-m_(2)n_(1))=(y-y_(1))/(n_(1)l_(2)-n_(2)l_(1))=(z-z_(1))/(l_(1)m_(2)-l_(2)m_(1))

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

Show that the equation of the plane through the line x/l=y/m=z/n and perpendicular to the plane containing non perpendicular lines x/m=y/n=z/l and x/n=y/l=z/m is (m-n)x+(-l)y+(l-m)z=0 .

If (x-1)/l=(y-2)/m=(z+1)/n is the equation of the line through (1,2,-1) and (-1,0,1) , then (l,m,n)

The direction ratios of the bisector of the angle between the lines whose direction cosines are l_1,m_1,n_1 and l_2,m_2,n_2 are (A) l_1+l_2,m_1+m_2+n_1+n_2 (B) l_1-l_2,m_1-m_2-n_1-n_2 (C) l_1m_2-l_2m_1,m_1n_2-m_2n_1,n_1l_2-n_2l_1 (D) l_1m_2+l_2m_1,m_1n_2+m_2n_1,n_1l_2+n_2l_1

The direction ratios of the bisector of the angle between the lines whose direction cosines are l_1,m_1,n_1 and l_2,m_2,n_2 are (A) l_1+l_2,m_1+m_2+n_1+n_2 (B) l_1-l_2,m_1-m_2-n_1-n_2 (C) l_1m_2-l_2m_1,m_1n_2-m_2n_1,n_1l_2-n_2l_1 (D) l_1m_2+l_2m_1,m_1n_2+m_2n_1,n_1l_2+n_2l_1

If (x-1)/(l)=(y-2)/(m)=(z+1)/(n) is the equation of the line through (1,2,-1) and (-1,0,1) then (l,m,n)