Example 4. Determine the point $B$, which is the end of the vector $\vec{a}=\{3,-4,2\}$, if its beginning coincides with the point $A(2,-1,1)$.
Solution. Let point $B$ have coordinates $B(x, y, z)$ (Fig. 3.6). Then the coordinates of the vector (point $1^{\circ}$)

$$
\overrightarrow{A B}=\vec{a}=\{x-2, y-(-1), z-1\}=\{3,-4,2\}
$$

![](https://cdn.mathpix.com/cropped/2024_05_22_8f5be56c3f01f571fd60g-036.jpg?height=136&width=297&top_left_y=285&top_left_x=2140)

Fig. 3.6
Therefore, $x-2=3 ; y+1=-4 ; z-1=2$.

Answer. $B(5,-5,3)$.