Vector and cartesian equation of line

Find the vector and cartesian equation of a line passes through the points (1,3,2) and origin.

Find the vector equation and cartesian equation of a line passing through the points A(3 ,4, -7) and B(6, -1, 1)

Find the vector and cartesian equations of the line that passes through : (i) the origin and (5, -2, 3) (ii) the points (1,2,3) and (2,-1,4)

(i) Find the vector and cartesian equation of the line passing through the point (1,2,-4) and perpendicular to the two lines : (x - 8)/(3) = (y + 19)/(-16) = (z - 10)/(7) and (x - 15)/(3) = (y - 19)/(8) = (z - 5)/(-5) . (ii) Find the vector and cartesian equations of the line passing through the point (2,1,3) and perpendicular to the lines : (x -1)/(1) = (y -2)/(2) = (z - 3)/(3) and (x)/(-3) = (y)/(2) = (z)/(5) .

Find the vector and cartesian equation of the line passing through the point P (1,2,3) and parallel to the planes : vec(r).(hati - hatj + 2 hatk) = 5. vec(r).(3hati + hatj + hatk) = 6.

Find the Vector and Cartesian equations of the line passing through the point (1,2,4) and perpendicular to the two lines (x-8)/(3)=(y+19)/(-16)=(z-10)/(7) and (x-15)/(3)=(y-29)/(8)=(z-5)/(-5)

Find the vector and cartesian equations of the line passing through the point P(1,2,3) and parallel to the planes vec r*(hat i-hat j+2hat k)=5 and vec r*(3hat i+hat j+hat k)=6

Find the vector and cartesian equations of the plane which passes through the point (5," "2," "" "4) and perpendicular to the line with direction ratios (2," "3," "" "1) .

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