Question

Find the initial point of the vector that is equivalent to $\mathbf{u}=(1,1,3)$ and whose terminal point is $B(-1,-1,2)$.

Answer 1

The initial point of a vector is the point that the vector starts from or originates from. To find the initial point of a vector, we need to subtract the vector from the terminal point of the vector.

In this case, the terminal point of the vector is given as $B(-1,-1,2)$, and the vector is given as $\mathbf{u} = (1,1,3)$. To find the initial point, we simply subtract the coordinates of the vector from the coordinates of the terminal point, like this:

$$\begin{aligned} B - \mathbf{u} &= (-1,-1,2) - (1,1,3) \ &= (-1 - 1,-1 - 1,2 - 3) \ &= (-2,-2,-1) \end{aligned}$$

Therefore, the initial point of the vector is $\boxed{(-2,-2,-1)}$.