Three forces are acting simultaneously at one point. Two forces P… - Vidyadip

MCQ

Three forces are acting simultaneously at one point. Two forces $\overrightarrow{ P }, \overrightarrow{ Q }$ are $(2 \hat{i}-3 \hat{j})$ and $(\hat{i}-\hat{j})$ respectively. If the object is in equilibrium then which will be the third:

A
$i-2 j$
✓
$-3 i+4 j$
C
$2 \hat{i}-2 \hat{j}$
D
$3 \hat{i}+4 \hat{j}$

✓

Answer

Correct option: B.

$-3 i+4 j$

(B)Forequilibrium
$
\begin{aligned}
\overrightarrow{P}+\overrightarrow{Q}+\overrightarrow{R} & =0 \\
\overrightarrow{R} & =-(\overrightarrow{P}+\overrightarrow{Q}) \\
& =-(2 \hat{i}-3 \hat{j}+\hat{i}-\hat{j}) \\
& =-(3 \hat{i}-4 \hat{j}) \\
& =-3 i+4 j
\end{aligned}
$
Hence, the correct option is (B).

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