Question 89: Motion in 2D & Vectors

Question

The vector sum of two forces $\vec{A}$ and $\vec{B}$ is perpendicular to their vector difference. Hence forces $\vec{A}$ and $\vec{B}$ are

Accepted Answer

The sum of the two forces,
$$ \overrightarrow{F_1}=\vec{A}+\vec{B} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...(i)$$
The difference of the two forces,
$$ \vec{F}_2=\vec{A}-\vec{B} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...(ii)$$
Since sum of the two forces is perpendicular to their difference,
$$ \begin{aligned} & \vec{F}_1 \cdot \vec{F}_2=0 \ \Rightarrow \quad & (\vec{A}+\vec{B}) \cdot(\vec{A}-\vec{B})=0 \ \Rightarrow \quad & A^2-\vec{A} \cdot \vec{B}+\vec{B} \cdot \vec{A}-B^2=0 \ 	herefore \quad & A^2=B^2 \Rightarrow|A|=|B| \end{aligned} $$
Thus, the forces are equal to each other in magnitude.

Answer

perpendicular to each other.

Answer

parallel to each other.

Answer

unequal in magnitude.

Answer

equal in magnitude.

Motion in 2D & Vectors

The vector sum of two forces \vec{A} and \vec{B} is perpendicular to their vector difference. Hence forces \vec{A} and \vec{B} are

Choose the correct answer: