Given the vector \( \mathbf{T} \) with an initial position (-2, 4) and a terminal point (-10, 6), express it in component form.

To find the component form of vector \( \mathbf{T} \), we subtract the initial position from the terminal point:

\( \mathbf{T} = \begin{bmatrix} -10 - (-2) \\ 6 - 4 \end{bmatrix} = \begin{bmatrix} -8 \\ 2 \end{bmatrix} \)

Therefore, the vector \( \mathbf{T} \) in component form is \( \begin{bmatrix} -8 \\ 2 \end{bmatrix} \).

The component form of a vector \(\mathbf{T}\) with an initial point \((x_1, y_1)\) and a terminal point \((x_2, y_2)\) is given by

$$\mathbf{T}=\langle x_2-x_1, y_2-y_1 \rangle$$

Thus, for the given vector \(\mathbf{T}\), we have

$$\mathbf{T}=\langle -10-(-2), 6-4 \rangle = \langle -8, 2 \rangle$$