To write the component form of the vector describing the straight-line path from the car's current position $C(4, -12)$ to its intended destination $D(10, -15)$, we use the formula for the component form of a vector between two points $C(x_1, y_1)$ and $D(x_2, y_2)$:

$\text{Vector } \overrightarrow{CD} = (x_2 - x_1, y_2 - y_1)$

Substituting the coordinates of $C(4, -12)$ and $D(10, -15)$:

$\overrightarrow{CD} = (10 - 4, -15 - (-12)) = (6, -3)$

Thus, the component form of the vector from $C$ to $D$ is $\overrightarrow{CD} = (6, -3)$.

Would you like further details or clarifications?

Here are 5 related questions to explore further:

1. How can you find the magnitude of the vector $\overrightarrow{CD}$?
2. How do you convert a vector from component form to unit vector form?
3. What is the direction angle of the vector $\overrightarrow{CD}$?
4. How would the vector change if the destination point $D$ were different?
5. Can you describe the relationship between vector components and vector magnitude?

Tip: To find the direction of a vector, use the arctangent function to calculate the angle it makes with the positive x-axis.