The points ${P}$ and ${Q}$ have position vectors ${\mathbf{a} + \mathbf{b}}$ and \({3\mathbf{a

Question

The points ${P}$ and ${Q}$ have position vectors ${\mathbf{a} + \mathbf{b}}$ and ${3\mathbf{a} - 2\mathbf{b}}$ respectively relative to the origin ${O}$. Given that ${OPQR}$ is a parallelogram, express the vectors ${\overrightarrow{PQ}}$ and ${\overrightarrow{PR}}$ in terms of ${\mathbf{a}}$ and ${\mathbf{b}}$. By evaluating two scalar products, show that if ${OPQR}$ is a square, then ${\left| \mathbf{a} \right|^2 = 2\left| \mathbf{b} \right|^2}$.

Accepted Answer

$\overrightarrow{PQ}=2\mathbf{a}-3\mathbf{b}$, $\overrightarrow{PR}=\mathbf{a}-4\mathbf{b}$

RI Vectors Tutorial Q9

RI Vectors Tutorial Q9

Video Solution: