Find the vector and the cartesian equations of the line that passes through the points (3,-2,-5), (3,-2,6).

Find the vector and the cartesian equations of the lines that pass through the origin and (5,-2,3).

Find the vector and Cartesian equation of the line pasing through the points (3,4,-7) and (5,1,6)

Find the vector and cartesian equations of the plane passing through the points A(1, -2, 3) and B(-1,2,-1) and is parallel to the line (x-2)/(2)=(y+1)/(3)=(z-1)/(4) .

Find the vector and cartesian equations of the plane that passes through the point (1,0,-2) and normal to hati+hatj-hatk .

Find the vector and cartesian equations of the planes a. that passes through the point (1,0,-2) and normal to the planes is hati+hatj-hatk b. that passes through the point (1,4,6) and the normal vector to the plane is hati-2hatj+hatk .

Find the equation of the plane that passes through three points : (1,1,-1),(6,4,-5),(-4,-2,3) .

Find the vector cartesian equation of the plane passing through the points (1, -2, 3) and (-1, 2, -1) and is parallel to the line vecr=(2hati-hatj+hatk)+t(2hati+3hatj+4hatk)

Consider the points A(2,2,-1) , B(3,4,2) and C(7,0,6) i.Find AB. ii. Find the vector and cartesian equation of the plane passing through these points .

Find the Cartesian equation of a line passing through the points A(2,-1,3)andB(4,2,1)

Find the vector and cartesian equations of the plane passing through the point (-1,3,2) and perpendicular to the planes.x + 2y + 2=5 and 3x+y+2z=8.