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`

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

Find the equations of a straight line which passes through the point (-1,0,0) and is parallel to the straight line (2x-1)/(4)=3(y)/(2)=(z-1)/(1)

Find the equations of the line passing through the point (3,0,1) parallel to the planes x+2y=0 and 3y-z=0 .

Find an equation or the line that passes through the point P(2,\ 3,\ 1) and is parallel to the line of intersection o the planes x+2y-3z=4\ a n d\ x-2y+z=0 .

Find the Cartesian and vector equation of the plane passing through the point (2,0,-1) and parallel to to the lines. x/-3=(y-2)/4=z+1 and x-4=(1-y)/2=2z .

Find the equation of the plane whch passes through the line a_1x+b_1y+c_1y+c_1z+d_1=0 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

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

Find the equation of a line passing through (1,-1,0) and parallel to the line (x-2)/(3)=(2y+1)/(2)=(5-z)/(1)

Let the equations of two planes be P_1: 2x-y+z=2 and P_2: x+2y-z=3 Equation of the plane which passes through the point (-1,3,2) and is perpendicular to each of the plane P_1 and P_2 is (A) x-3y-5z+20=0 (B) x+3y+5z-18=0 (C) x-3y-5z=0 (D) x+3y-5z=0