newtonian mechanics - What is the direction of gravitational constant?

Our book says:

$$\vec F=\dfrac{GMm}{r^2}$$

If Force is a vector quantity, $G$ must also be vector quantity so what is the direction of $G$.

I am a school kid please explain simply and kindly

Answer

$G$ is not a vector quantity, but just a number - a so-called scalar quantity - just like mass $m$. True, force is a vector quantity, but the formula you show here is a formula for the "size" of the force only!

The "size" or "strength" of a vector is called the magnitude. Some formulas give magnitudes only, other formulas give directions and yet other formulas give the full vector quantity including both its magnitude and direction. The formula you showed here does not give the direction, but only the magnitude of the force.

Compare these two formulas:

$$F=G\frac{Mm}{d^2}\qquad,\qquad \vec F=G\frac{Mm}{d^2}\hat r$$

The first formula gives the force magnitude $F$. That is the one you showed. The second gives the full force vector $\vec F$. In the second one, there is included a unit direction vector that points in the direction of the force, which I here call $\hat r$. (A unit vector is a vector with a magnitude of 1.) Without this, the direction is not involved at all because - as you rightfully question - none of the other parameters are vectors.

_{(You might here and there see other versions of this formula depending on how $\hat r$ is defined. For instance, on this Wikipedia page as well as in an answer below they have flipped $\hat r$ to mean the opposite of how I have used it, and then they add a minus sign so the formula still fits. And in another answer below, a different symbol $\mathbf e$ is used, which isn't a unit vector, so it must be divided by its length $d$ so it still fits (so that $\hat r=\frac{\mathbf e}d$). It is thus important that it is clear each time what such parameters exactly mean.)}