I'm having trouble finding a way to solve this particular problem:
The point $A$ moves on $\vec{g}$ from point $J$ to $G$ and is dependent on the real parameter $t$:
$\vec{g} = (-1/0/0) + t*(1/1/1)$
For which value of $t$ is point $A$ the closest to point $B (9/1/1)$?
The length of $\vec{BJ}$ is 4 units and the length of $\vec{BG}$ is 7 units. The angle between $\vec{BJ}$ and $\vec{BG}$ is 60°.
I know the length of $\vec{JG}$ is $\sqrt{37}$
But how do I find the value for $t$ for which point $A$ is the closest to point $B$?
Edit:
There seems to be some confusion concerning the provided values, so I'm giving the full scope of the problem presented in my textbook. The text describes $g$ as a straight line, on which are the points $J$ and $G$, which are fixed points, and point $A$, which moves between these two points.
The location of $A$ is described as: $\vec{g} = (-1, 0, 0) + t*(1, 1, 1)$, which is why I thought this was primarily about vectors.
Then there's point $B$, which is at $(9, 1, 1)$. The distance from $B$ to $J$ is defined as 4 units and the distance from $B$ to $G$ is 7 units. The angle enclosed by $BJ$ and $BG$ is $60$°.
In the first partial problem I was asked to find the length between $JG$, which is $\sqrt{37}$.
Then in the second partial problem, which is the topic of the question posted here, I'm asked for which value of $t$ on the straight line $g$ is point $A$ the closest to point $B$.
That's all the info available to me.