# Math Help - Vector- closest to the point

1. ## Vector- closest to the point

The line l has vector equation r=2i+s(i+3j+4k), Determine the position vector of the point on l which is closest to the point with position vector 6i-j+3k

urgent

2. Originally Posted by kingkaisai2
The line l has vector equation r=2i+s(i+3j+4k), Determine the position vector of the point on l which is closest to the point with position vector 6i-j+3k

urgent
Write $\bold v=\bold{i}+3\bold{j}+4\bold{k}$, $\bold r(s)=2\bold i+s\bold v$ and $\bold x=6\bold i-\bold j+3\bold k$.

Then solve:

$\bold v\cdot (\bold r(s)-\bold x)=0$

for $s$, which should work as $\bold v$ is a vector pointing along the line,
and the vector from $\bold x$ to the closest point on the line is at orthogonal to $\bold v$.

RonL