AP EAMCET · PHYSICS · Mathematics in Physics
The resultant of two vectors \(\vec{A}\) and \(\vec{B}\) is perpendicular to vector \(\vec{A}\) and the resultant magnitude is equal to half of the magnitude of \(\vec{B}\), then the angle between \(\vec{A}\) and \(\vec{B}\) is
- A \(30^{\circ}\)
- B \(60^{\circ}\)
- C \(150^{\circ}\)
- D \(120^{\circ}\)
Answer & Solution
Correct Answer
(C) \(150^{\circ}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \vec{R}=\vec{A}+\vec{B} \\ & R=\frac{|\vec{B}|}{2} \\ & \frac{|\vec{B}|}{2}=\sqrt{A^2+B^2+2 A B \cos \theta} \\ & A^2+B^2+2 A B \cos \theta=\frac{B^2}{4} \\ & A^2+2 A B \cos \theta+\frac{3 B^2}{4}=0...(i) \\ & \vec{R} \perp \text { to } \vec{A} \\ & \vec{A}…
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