Determine whether the lines given by the vector equations r1=2i+3j+k+s(4i−k) and r2=2i+3j+k+t(2i+2j+k) intersect. If they intersect, give the coordinates of their point of intersection.

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?