Question

The vector \(v\) and its initial point are given. Find the terminal point. \(\mathbf{v}=\left\langle 1,-\frac{2}{3}, \frac{1}{2}\right\rangle\) Initial point: \(\left(0,2, \frac{5}{2}\right)\)

Short answer

The terminal point of the vector is (1, 2/3, 3).

Step-by-step solution

Identify the initial point and the vector components

The initial point of the vector is given as (0,2,5/2). The components of the vector \(v\) are given as \( \left\langle 1,-\frac{2}{3}, \frac{1}{2}\right\rangle \).

Add the vector's components to the initial point coordinates

To find the terminal point, each component of the vector is added to the corresponding coordinate of the initial point. That is, the terminal point is found by performing the following addition: (0+1, 2-(2/3), (5/2)+(1/2)) = (1, 2/3, 3).

Write down the Terminal Point

The terminal point of the vector \(v\), given its initial point and the vector's components, is thus found to be (1, 2/3, 3).