Find the vector and cartesian equations of the straight line passing through (-5, 2, 3) and (4, -3, 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 straight line passing through the point A with position vector 3veci-vecj+4veck and parallel to the vector -5veci+7vecj+3veck .

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

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)

Find the vector and cartesian equation of the plane passing through (2, -1, -3) and botr to the planes 3x+2y-4z=1 and 2x+3y+2z=7 .

Find the vector and cartesian equation of the plane passing through (2, -1, -3) and parallel to the line (x-5)/(3)=(y+1)/(2)=(z-3)/(-4) and (x+10)/(2)=(y-10)/(3)=(z-2)/(2)

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

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