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If vectors A=cos wti + sin wtj and B= cos wt/2 i + sin wt/2 j are functions of time, then the value of t at which they are orthogonal to each other is
Options
(a) t = π/2w
(b) t = π/w
(c) t=0
(d) t = π/4w
Correct Answer:
t = π/w
Explanation:
Two vectors are,
A = cos ωt î + sin ωt ĵ
B = cos (ωt/2) î + sin (ωt/2) ĵ
For two vectors A and B to be orthogonal
A.B = 0
A.B = 0 = cos ωt.cos (ωt/2) + sin ωt.sin (ωt/2)
= cos [ωt – (ωt/2)] = cos (ωt/2)
So, ωt/2 = π/2
.·. t = π/ω.
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Topics: Motion in Plane
(93)
Subject: Physics
(2479)
Important MCQs Based on Medical Entrance Examinations To Improve Your NEET Score
- A concave mirror of focal length f₁ is placed at a distance d from a convex lens
- A stone falls freely under gravity.It covers distances h₁,h₂ and h₃
- A conveyor belt is moving at a constant speed of 2 m/s. A box is gently dropped on it
- The first line in Lyman series has wavelength λ. The wavelength
- If 10000 V is applied across an X-ray tube, what will be the ratio of de-Broglie
Topics: Motion in Plane (93)
Subject: Physics (2479)
Important MCQs Based on Medical Entrance Examinations To Improve Your NEET Score
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