Three vectors of magnitude `a ,2a ,3a` meet in a point and their directions are along the diagonals of the adjacent faces of a cube. Determine their resultant.

Explanation

To determine the resultant of three vectors of magnitudes \( a \), \( 2a \), and \( 3a \) that meet at a point and are directed along the diagonals of adjacent faces of a cube, we can follow these steps:

### Step 1: Define the Vectors
We need to visualize the cube and define the vectors based on their directions. The three vectors can be defined as follows:
- Let \( \vec{p} \) be the vector of magnitude \( a \) along the diagonal of the face in the x-z plane.
- Let \( \vec{q} \) be the vector of magnitude \( 2a \) along the diagonal of the face in the y-z plane.
- Let \( \vec{r} \) be the vector of magnitude \( 3a \) along the diagonal of the face in the x-y plane.

...