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NEET 2003
Exam
NEET
Year
2003
Subject
Physics
Chapter
Mathematics in Physics

NEET 2003 · Physics · Mathematics in Physics

The vector sum of two forces is perpendicular to their vector...

The vector sum of two forces is perpendicular to their vector differences. In that case, the force:

Options

  1. Aare equal to each other
  2. Bare equal to each other in magnitude
  3. Care not equal to each other in magnitude
  4. Dcannot be predicted

Correct answer

B. are equal to each other in magnitude

Step-by-step solution

(A⃗+B⃗)⋅(A⃗−B⃗)=0(\vec{A}+\vec{B}) \cdot(\vec{A}-\vec{B})=0⇒A2−A⃗⋅B⃗+B⃗⋅A⃗+B2=0⇒A=B(∵A⃗⋅B⃗=B⃗⋅A⃗)\begin{aligned} & \Rightarrow A^2-\vec{A} \cdot \vec{B}+\vec{B} \cdot \vec{A}+B^2=0 \\ & \Rightarrow \mathrm{A}=\mathrm{B} \quad(\because \vec{A} \cdot \vec{B}=\vec{B} \cdot \vec{A}) \end{aligned}$$
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