# Unit vector in the xy-plane that makes an angle of 45o with the vector i + j and an angle of 60o with the vector 3i - 4j is A. i B. 2i C. v2i D. none of the above

SHAIK AASIF AHAMED
8 years ago
let the unit vector be of the form ai+bj
as it is a unit vector a2+b2=1..............(1)
as it is making an angle of 45 with i+j
$cos 45=\frac{a+b}{sqrt(2)}$
so a+b=1......................(2)
from 1 and 2 we get ab=0;
also it is making an angle of 60 with 3i-4j
$cos 60=\frac{3a-4b}{5}$
3a-4b=2.5.........(3)
As there is no equation satisfying 1,2,3 simultaneously there is no such vector
Hence D is the correct answer
Thanks and Regards
Shaik Aasif