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Write the component form of the vector that describes the straight-line path from the car’s current position C to its intended destination D

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.

Write the component form of the vector that describes the straight-line path from the car’s current position C to its intended destination D.

Learn how to find the component form of the vector that describes the straight-line path from C(4, -12) to D(10, -15) using vector algebra. This example covers key concepts in vector calculations and is suitable for students in Grades 9-11.

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