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.
(1,0,0)which is your X-axis (assume front one). In this case, rotating along Z-axis (vertical axis) means you rotate the vector around Y-axis (right one). In another case let's say the vector is (0,1,0). Now rotating along Z means you rotate around X-axis. What exactly do you want in both cases? What happens when the vector is random? $\endgroup$