Thank you for the suggestions provided. As @gallickgunner mentioned, I shall rephrase the question will all the possible information which I could provide. I had attached also the schematic to depict my question.
1)I need to rotate the vector V with the base point P by an angle and find the new vector V'.
2) The rotation axis is say for is about a local y axis at point P (which is parallel to global Y axis)
3) Subsequently, I need to rotate the initial vector V about x axis which is parallel to global Y axis.
The main reason for the rotation is to find the new vector V' at point P. Both the rotations are independent and each of the rotation provides a new V'.
Thank you for the support. Looking forward for an answer at the earliest.