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)`

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))

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 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)

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

ABC is a right-angled triangle in which angleB=90^(@) and BC=a. If n points L_(1),L_(2),…,L_(n) on AB is divided in n+1 equal parts and L_(1)M_(1), L_(2)M_(2),…,L_(n)M_(n) are line segments paralllel to BC and M_(1), M_(2),….,M_(n) are on AC, then the sum of the lengths of L_(1)M_(1), L_(2)M_(2),...,L_(n)M_(n) is

ABC is a right-angled triangle in which angleB=90^(@) and BC=a. If n points L_(1),L_(2),…,L_(n) on AB is divided in n+1 equal parts and L_(1)M_(1), L_(2)M_(2),…,L_(n)M_(n) are line segments paralllel to BC and M_(1), M_(2),….,M_(n) are on AC, then the sum of the lengths of L_(1)M_(1), L_(2)M_(2),...,L_(n)M_(n) is

ABC is a right-angled triangle in which angleB=90^(@) and BC=a. If n points L_(1),L_(2),…,L_(n) on AB is divided in n+1 equal parts and L_(1)M_(1), L_(2)M_(2),…,L_(n)M_(n) are line segments paralllel to BC and M_(1), M_(2),….,M_(n) are on AC, then the sum of the lengths of L_(1)M_(1), L_(2)M_(2),...,L_(n)M_(n) is