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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

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

Grade:Upto college level

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 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
askIITians Faculty

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