The vector sum of two forces is perpendicular | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the two forces be $\vec{A}$ and $\vec{B}$.The vector sum is $\vec{P} = \vec{A} + \vec{B}$.The vector difference is $\vec{Q} = \vec{A} - \vec{B

Vedclass · Accepted Answer

are equal to each other in magnitude

Vedclass · Answer

(C) Let the two forces be $\vec{A}$ and $\vec{B}$.The vector sum is $\vec{P} = \vec{A} + \vec{B}$.The vector difference is $\vec{Q} = \vec{A} - \vec{B}$.Since $\vec{P}$ and $\vec{Q}$ are perpendicular,their dot product must be zero:$\vec{P} \cdot \vec{Q} = 0$Substituting the expressions for $\vec{P}$ and $\vec{Q}$:$(\vec{A} + \vec{B}) \cdot (\vec{A} - \vec{B}) = 0$Expanding the dot product:$\vec{A} \cdot \vec{A} - \vec{A} \cdot \vec{B} + \vec{B} \cdot \vec{A} - \vec{B} \cdot \vec{B} = 0$Since $\vec{A} \cdot \vec{B} = \vec{B} \cdot \vec{A}$,the middle terms cancel out:$|A|^2 - |B|^2 = 0$$|A|^2 = |B|^2$$|A| = |B|$Therefore,the forces are equal to each other in magnitude.

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

Similar Questions

In the process of transcription,the sigma factor is important for:

Which of the following magnetic properties is exhibited by the compounds of alkaline earth metals?

During joint diastole,..........

The rate of the reaction $2N_2O_5 \to 4NO_2 + O_2$ can be written in three ways:
$-\frac{d[N_2O_5]}{dt} = k[N_2O_5]$
$\frac{d[NO_2]}{dt} = k'[N_2O_5]$
$\frac{d[O_2]}{dt} = k''[N_2O_5]$
The relationship between $k$ and $k'$ and between $k$ and $k''$ are:

Which of the following is associated with pneumonia?

Vedclass Test Series

Exam Paper Generator

Online Exam Module