Question

The position coordinates of a particle moving in x-y plane changes from (1 m, 1 m) to (3 m, –5 m). Its displacement vector is represented as

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Points are (m,m) and (3m,-5m)}$

$\underline{\textsf{To find:}}$

$\textsf{The displacement vector}$

$\underline{\textsf{Solution:}}$

$\textsf{Let the given points be A(m,m) and B(3m,-5m)}$

$\textsf{Then,}$

$\mathsf{\overrightarrow{OA}=m\overrightarrow{i}+m\overrightarrow{j}}$

$\mathsf{\overrightarrow{OB}=3m\overrightarrow{i}-5m\overrightarrow{j}}$

$\textsf{Now,}$

$\textsf{Displacement vector}$

$\mathsf{\overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}}$

$\mathsf{\overrightarrow{AB}=(3m\overrightarrow{i}-5m\overrightarrow{j})-(m\overrightarrow{i}+m\overrightarrow{j})}$

$\mathsf{\overrightarrow{AB}=2m\overrightarrow{i}-6m\overrightarrow{j}}$

$\underline{\textsf{Answer:}}$

$\textsf{Displacement vector is}$

$\mathsf{2m\overrightarrow{i}-6m\overrightarrow{j}}$

Answer 2

$\underline{\textsf{Solution:}}$

$\textsf{Let the given points be A(m,m) and B(3m,-5m)}$

$\textsf{Then,}$

$\mathsf{\overrightarrow{OA}=m\overrightarrow{i}+m\overrightarrow{j}}$

$\mathsf{\overrightarrow{OB}=3m\overrightarrow{i}-5m\overrightarrow{j}}$

$\textsf{Now,}$

$\textsf{Displacement vector}$

$\mathsf{\overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}}$

$\mathsf{\overrightarrow{AB}=(3m\overrightarrow{i}-5m\overrightarrow{j})-(m\overrightarrow{i}+m\overrightarrow{j})}$

$\mathsf{\overrightarrow{AB}=2m\overrightarrow{i}-6m\overrightarrow{j}}$

$\underline{\textsf{Answer:}}$

$\textsf{Displacement vector is}$

$\mathsf{2m\overrightarrow{i}-6m\overrightarrow{j}}$