The line $l$ passes through the points $A\left( 2,-1,5 \right)$ and $B\left( -1,-4,2 \right)$. Find

Question

The line $l$ passes through the points $A\left( 2,-1,5 \right)$ and $B\left( -1,-4,2 \right)$. Find an equation of the line $l$. Given that $P$ is the point $\left( 4,5,3 \right)$, find the projection vector of $\overrightarrow{AP}$ onto $l$. Hence find the position vector of the foot of the perpendicular from the point $P$ to $l$.

Accepted Answer

(i) $\mathbf{r} = \begin{pmatrix} 2 \\ -1 \\ 5 \end{pmatrix} + \lambda\begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix}$ (ii) $F = (4, 1, 7)$

NJC Vectors II Tutorial Q4

NJC Vectors II Tutorial Q4

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