Question

❤️If vectors
A = cos ωt i + sin ωt j and B=cos ωt/2 i+sin ωt/2 j are functions of time, then the value of t at
which they are orthogonal to each other is:
(1) t = 0
(2) t = π/4ω
(3) t = π/2ω
(4) t = π/ω 

Please answer quickly. No spams required

Answer 1

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(4) t = π/w

step-by-step explanation:

given,

vector A = cos ωt i + sin ωt j

and

vector B = cos ωt/2 i + sin ωt/2 j

Now,

It is given that they are orthogonal

It means they are perpendicular to each other.

It means the dot product will be equal to zero,

as A•B = |A||B| cos 90°

but cos 90° = 0

=> |A||B| = 0

=> (cos ωt i + sin ωt j )•(cos ωt/2 i + sin ωt/2 j)=0

since im dot product only same axis results

=> (cos wt × cos wt/2) + (sin wt × sin wt/2) = 0

further solving the equation,

we get

(4) t = π/w