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Mathematics · 2022 · 2 marks
CBSE 2022 · Region 1 · Set 1 · Q2
In a parallelogram PQRS, PQ =3 i -2 j +2 k and PS =- i -2 k. Find | PR | and | QS |.
In a parallelogram $\displaystyle \mathrm{PQRS}, \overrightarrow{\mathrm{PQ}}=3 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}$ and $\displaystyle \overrightarrow{\mathrm{PS}}=-\hat{\mathrm{i}}-2 \hat{\mathrm{k}}$. Find $\displaystyle |\overrightarrow{\mathrm{PR}}|$ and $\displaystyle |\overrightarrow{\mathrm{QS}}|$.
Marking-scheme solution
\[\begin{aligned}
& \overrightarrow{P R}=\overrightarrow{P Q}+\overrightarrow{P S} \because \overrightarrow{P S}=\overrightarrow{Q R} \\
& \quad=2 \hat{i}-2 \hat{j} \\
& |\overrightarrow{P R}|=2 \sqrt{2} \\
& \overrightarrow{Q S}=\overrightarrow{Q P}+\overrightarrow{P S}=\overrightarrow{P S}-\overrightarrow{P Q} \\
& =-4 \hat{i}+2 \hat{j}-4 \hat{k} \\
& |\overrightarrow{Q S}|=6
\end{aligned}
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