Find a unit vector perpendicular to each of the vectors and where and

Solve the following differential equation:

e^x tan y dx +(1 – e^x) sec² y dy = 0

Solve the following differential equation:

Find the angle between the following pair of lines:

and

and check whether the lines are parallel or perpendicular.

Probabilities of solving a specific problem independently by A and B are and respectively. If both try to solve the problem independently, find the probability that (i) theproblem is solved (ii) exactly one of them solves the problem.