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To find the terminal point of a vector \( \vec{v} = (1, 2, 4) \) that has an initial point \( (-9, 15, -6) \), we add the components of the vector \( \vec{v} \) to the coordinates of the initial point.

Let the initial point be \( (x_1, y_1, z_1) = (-9, 15, -6) \) and the vector components be \( \vec{v} = (1, 2, 4) \).

The terminal point \( (x_2, y_2, z_2) \) can be found by:
\[
x_2 = x_1 + 1 = -9 + 1 = -8
\]
\[
y_2 = y_1 + 2 = 15 + 2 = 17
\]
\[
z_2 = z_1 + 4 = -6 + 4 = -2
\]

So, the terminal point is:
\[
(x_2, y_2, z_2) = (-8, 17, -2)
\]

### Answer:
The terminal point is \( (-8, 17, -2) \).

Would you like more details, or do you have any questions?

### Related Questions:
1. How do you calculate the length (magnitude) of a vector?
2. What is the difference between initial and terminal points in vector terminology?
3. How can you find a unit vector in the same direction as a given vector?
4. How do you add two vectors in three-dimensional space?
5. How do you determine if two vectors are perpendicular?

### Tip:
When given a vector and an initial point, always add each component of the vector to the corresponding coordinate of the initial point to find the terminal point.

Vector \( \vec{v} = (1, 2, 4) \) has initial point \( (-9, 15, -6) \). Find the terminal point.

This page provides a step-by-step solution to find the terminal point of a vector \( \vec{v} = (1, 2, 4) \) with an initial point at \( (-9, 15, -6) \). Understand the vector addition formula used in coordinate geometry, suitable for high school students in Grades 10-12.

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