A vector a has components 1 and 2 p with respect to a rectangular Cartesian system. This system is rotated through a certain angle about origin in the counter clock wise sense. If, with respect to the new system, a has components 1 and (p+1) , then

Step-by-step solution

aligned a & =1 i +2 p j & = i +2 p j aligned Let b be the vector obtained on rotation with components 1 and (p+1) . Then, aligned & b = i +( p +1) j & | a |=| b | aligned ...[Magnitude remains unchanged after rotation] aligned & | a |^2=| b |^2 & 1+(2 p)^2=1+(p+1)^2 & 4 p^2=p^2+2 p+1 & 3 p^2-2 p-1=0 & (3 p+1)(p-1)=0 & p=- 1 3 or p=1 aligned