Question

In a parallelogram PQRS, PQ vector = 3î - 2j + 2k and PS Vector = -î - 2k. Find |vector PR| and |vector QS|.

Answer 1

\(\overrightarrow{PQ}=3\hat i-2\hat j+2\hat k\)

\(\overrightarrow{PS}=3\hat i-2\hat k\)

By triangle formula of vectors, we get

\(\overrightarrow{PQ}+​​​​\overrightarrow{QS}=\overrightarrow{PS}\)

⇒ \(\overrightarrow{QS}=\overrightarrow{PS}-\overrightarrow{PQ}\)

 = (-\(\hat i-2\hat k\)) - (\(3\hat i-2\hat j+2\hat k\))

 = \(-4\hat i+2\hat j-4\hat k\)

\(|\overrightarrow{QS}=\sqrt{16+4+16}|\) = \(\sqrt{36}\) = 6