If are mutually perpendicular vectors of equal magnitudes, show that the vector is equally inclined to and Also, find the angle which makes with or or

Prove that is the general solution of the differential equation where C is a parameter.

Let and then

A. Let and find which makes and coplanar.

B. If and show that no value of can makes and coplanar.

The random variable X can take only the values 0, 1, 2, 3. Given that and such that find the value of p.

Often it is taken that a truthful person commands, more respect in the society. A man is known to speak the truth 4 out of 5 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.

Do you also agree that the value of truthfulness leads to more respect in society?