JEE Main & Advanced
Mathematics
Vector Algebra
Question Bank
Critical Thinking
question_answer
A vector a has components 2p and 1 with respect to a rectangular cartesian system. The system is rotated through a certain angle about the origin in the anti-clockwise sense. If a has components p+1 and 1 with respect to the new system, then [IIT 1984]
A)\[p=0\]
B)\[p=1\] or \[-\frac{1}{3}\]
C)\[p=-1\] or \[\frac{1}{3}\]
D)\[p=1\] or \[-1\]
Correct Answer:
B
Solution :
If \[x,\,\,y\] are the original components; \[X,\,\,Y\]the new components and \[\alpha \] is the angle of rotation, then \[x=X\cos \alpha -Y\sin \alpha \] and \[y=X\sin \alpha +Y\cos \alpha \]