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?
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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.