Find the vector equation of the line through the points `(1,-2,1) and (0,-2,3)`.

Find the vector equation of the line passing through the point A(1, 2, –1) and parallel to the line 5x – 25 = 14 – 7y = 35z .

Find the vector equation for the line passing through the points (1, 0, 2) and (3, 4, 6) .

Find the vector equation of the line passing through the point (1,-1,2) and perpendicular to the plane 2 x-y+3z-5=0.

Find the vector equation of the line passing through the point (1,-1,2) and perpendicular to the plane 4x-2y-5z-2=0.

find the vector equation of the line passing through the point A(2,-1,1) and parallel to the ine joining the points B(-1,4,1) and C(1,2,2). Also find the Cartesian equation of the line.

Find the direction cosines of the line (x+2)/2=(2y-7)/6=(1-z)/(-3) . Also, find the vector equation of the line through the point A(-1,\ 2,\ 3) and parallel to the given line.

Find the vector equation of the plane passing through the points (1,1,0),(1,2,1)a n d(-2,2,-1)dot

Find the direction cosines of the line (x+2)/2=(2y-7)/6=(5-z)/6dot Also, find the vector equation of the line through the point A(-1,2,3) and parallel to the given line.

Find the equation of the line Passing through the points (-1, 1) , and (2, -4) .

Find the vector equation of the plane passing through the points (1, 1, -1), (6, 4, -5) and (-4, -2, 3).