Question

If vectors A^-->= cos wt i^{^} + sin wt j^{^} and B^--> = cos wt /2^{^}i + sin wt/2 j^{^} are functions of time, then value of t at which they are orthogonal to each other is:

Answer 1

Solution :
A→ . B→ = (coswti^+sinwtj^).(coswt2i^+sinwt2j^)

=cos(wt−wt/2)

When they are orthogonal A→ . B→=0

=> cos(wt−wt2)=0
cos(wt/2)=0
we know cos (π/2) = 0
wt/2=π/2
t=π/w
Answer : t=π/w

like if satisfied