Prove that the line through the point `(x_(1),y_(1))` and parallel to the line `Ax+By+C=0` is `A(x-x_(1)) +B(y-y_(1))=0`.

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

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

Find the vector equation of the line through the point (2,-1,-1) and is parallel to the line 6x-2=3y+1=2z-2 .

Find the equation of the lines through (- 2, -1) and are : parallel to line x = 0.

The equation of the line passing through (1,2) and perpendicular to the line x+y+1=0 is :

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

Find the equation of the plane through the point (0,0,0) and (3,-1,2) and parallel of the line (x-4)/1=(y+3)/-4=(z+1)/7

Find the equation of the plane through the point (0, 0, 0) and (3, -1 , 2) and parallel to the line. (x-4)/1=(y+3)/-4=(z+1)/7 .

The line (x-x_1)/a=(y-y_1)/b=(z-z_1)/c is parallel to the plane Ax+By+Cz+D =0 if

Find the combined equation of the straight lines passing through the point (1,1) and parallel to the lines represented by the equation . x^2-5xy+4y^2+x+2y-2=0 .