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Text Solution

p=0p=1 or `p=-(1)/(3)`p=-1 or `p=(1)/(3)`p=1 or `p=-1`

Answer :

BSolution :

We have, `a=2p hati+hatj` <br> Or rotation, let b be the vector with components (p+1) and 1 so that, <br> `b=(p+1)hati+hatj` <br> Now, `|a|=|b|impliesa^(2)=b^(2)` <br> `implies4p^(2)+1=(p+1)^(2)+1implies4p^(2)=(p+1)^(2)` <br> `implies2p=+-(p+1)implies3p=-1` or p=1 <br> `therefore p=-(1)/(3)` or p=1.