The position vectors of points $P$, $Q$ and $R$ relative to an origin $O$ are \(-4\mathbf{i}

Question

The position vectors of points $P$, $Q$ and $R$ relative to an origin $O$ are $-4\mathbf{i}-4\mathbf{j}$, $2\mathbf{i}+6\mathbf{j}$ and $5\mathbf{i}-2\mathbf{j}$ respectively. Find the exact perpendicular distance of the point $P$ from the line segment $QR$. the exact projection length of $\overrightarrow{QP}$ on $\overrightarrow{QR}$.

Accepted Answer

(i) $\dfrac{78}{\sqrt{73}}=\dfrac{78\sqrt{73}}{73}$ units (ii) $\dfrac{62}{\sqrt{73}}=\dfrac{62\sqrt{73}}{73}$ units

Vectors - Projection Lengths

Vectors - Projection Lengths

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