The two adjacent sides of a parallelogram are and Find the two-unit vectors parallel to its diagonals. Using the diagonal vectors, find the area of the parallelogram.

Find the vector equation of the plane with intercepts 3, -4 and 2 on x, y and z-axis respectively.

Find the coordinates of the point where the line through the points A(3, 4, 1) and B(5, 1, 6) crosses the XZ plane. Also find the angle which this line makes with the XZ plane.

In a game, a man wins ₹ 5 for getting a number greater than 4 and loses ₹ 1 otherwise, when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a number greater than 4. Find the expected value of the amount he wins/loses.

OR

A bag contains 4 balls. Two balls are drawn at random (without replacement) and are found to be white. What is the probability that all balls in the bag are white?

Differentiate with respect to x.

OR

If prove that