Write the vector equations of the following lines and hence determine the distance between them `(x-1)/(2) = (y-2)/(3) = (z+4)/(6)` and `(x-3)/(4) = (y-3)/(6) = (z+5)/(12)`.

Answer

`vec(r) = (hat(i) + 2hat(j) - 4hat(k)) + mu(2hat(i) + 3hat(j) + 6hat(k))` and `vec(r) = (3hat(i) + 3hat(j) - 5hat(k)) + lambda(4hat(i) + 6hat(j) + 12 hat(k)); (sqrt(293))/(7)` units