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 $\displaystyle \bold v=\bold{i}+3\bold{j}+4\bold{k}$, $\displaystyle \bold r(s)=2\bold i+s\bold v$ and $\displaystyle \bold x=6\bold i-\bold j+3\bold k$.Originally Posted by kingkaisai2
Then solve:
$\displaystyle \bold v\cdot (\bold r(s)-\bold x)=0$
for $\displaystyle s$, which should work as $\displaystyle \bold v$ is a vector pointing along the line,
and the vector from $\displaystyle \bold x$ to the closest point on the line is at orthogonal to $\displaystyle \bold v$.
RonL