Question

Compare the components for the following vector equations

(a) ${\displaystyle \text{T}\hat{j}-\text{mg}\hat{j}=\text{ma}\hat{j}}$
(b) ${\displaystyle \overrightarrow{T}+\overrightarrow{F}=\overrightarrow{A}+\overrightarrow{B}}$
(c) ${\displaystyle \overrightarrow{T}-\overrightarrow{F}=\overrightarrow{A}-\overrightarrow{B}}$
(d) ${\displaystyle \text{T}\hat{j}+\text{mg}\hat{j}=\text{ma}\hat{j}}$

Answer 1

Components of the vectors

(a) T – mg = ma

(b) ${\displaystyle {\overline{T}}_x+{\overline{F}}_x={\overline{A}}_x+{\overline{B}}_x}$ (Or)
${\displaystyle {\overline{T}}_y+{\overline{F}}_y={\overline{A}}_y+{\overline{B}}_y}$

(c) ${\displaystyle {\overline{T}}_x-{\overline{F}}_x={\overline{A}}_x+{\overline{B}}_x}$ (Or)
${\displaystyle {\overline{T}}_y-{\overline{F}}_y={\overline{A}}_y+{\overline{B}}_y}$

(d) T + mg = ma