Show that the equation of the straight line through `(alpha, beta)` and through the point of intersection of the lines `a_1x+b_1y+c_1=0 and a_2x+b_2y+ c_2 = 0` is `(a_1x+b_1y+c_1)/(a_1alpha+b_1beta+c_1)=(a_2x+b_2y+c_2)/(a_2alpha+b_2beta+c_2)`

Show that the equation of the straight line throught (alpha,beta) and through the point of intersection of the lines a_(1)x+b_(1)y+c_(1)=0 anda_(2)x+b_(2)y+c_(2)=0 is (a_(1)x+b_(1)y+c_(1))/(a_(1)alpha+b_(1)beta+c_(1))=(a_(2)x+b_(2)y+c_(2))/(a_(2)alpha+b_(2)beta+c_(2))

findthe equationof the plane passing through the point (alpha, beta, gamma) and perpendicular to the planes a_1x+b_1y+c_1z+d_1=0 and a_2x+b_2y+c_2z+d_2=0

findthe equationof the plane passing through the point (alpha, beta, gamma) and perpendicular to the planes a_1x+b_1y+c_1z+d_1=0 and a_2x+b_2+yc_2z+d_2=0

In the pair of linear equations a_1x+b_1y+c_1=0 and a_2x+ b_2y + C_2 = 0. If a_1/a_2 ne b_1/b_2 then the

Find the equation of the plane which passes through the line of intersection of the planes a_1x+b_1y+c_1z+d_1=0 and a_2x+b_2y+c_2z+d_2=0 and which is parallel to the line (x-alpha)/l=(y-beta)/m=(z-gamma)/n

Find the equation of the plane which passes through the line of intersection of the planes a_1x+b_1y+c_1z+d_1=0 and a_2x+b_2y+c_2z+d_2=0 and which is parallel to the line (x-alpha)/l=(y-beta)/m=(z-gamma)/n

Find the equation of the line which passes thorugh the point P(alpha, beta, gamma) and is parallel to the line a_1x+b_1y+c_1z+d_1=0, a_2x+b_2y+c_2z+d_2=0

Find the equation of the line which passes thorugh the point P(alpha, beta, gamma) and is parallel to the line a_1x+b_1y+c_1z+d_1=0, a_2x+b_2y+c_2z+d_2=0

a_1x+b_1y+c_1=0" and "a_2x+b_@y+c_2=0 are……..equations.

The pair of equations a_1x+b_1y+c_1=0" and "a_2x+b_2y+c_2=0 are consistent, then……..