Question

In Exercises 47 and \(48,\) the vector \(v\) and its initial point are given. Find the terminal point. \(\mathbf{v}=\langle 3,-5,6\rangle\) Initial point: (0,6,2)

Short answer

The terminal point of the vector \( \mathbf{v} \) is (3, 1, 8).

Step-by-step solution

Identify the Components of the Vector and Initial Point

The vector \( \mathbf{v} \) is given by \( \langle 3,-5,6 \rangle \) and the initial point is given by (0,6,2). The numbers 3, -5, and 6 are the x, y, and z components of the vector, respectively. The initial point represents the starting point where the vector is originating from.

Calculate Terminal Point Coordinates

Each component of the vector is added to the corresponding coordinate of the initial point. So, the terminal point P (x, y, z) of the vector will be given by:\n\n(x, y, z) = (0+3 , 6+(-5) , 2+6).

Simplify to Obtain the Terminal Point

Simplify the coordinates to obtain the terminal point: (x, y, z) = (3, 1, 8). So, the terminal point of vector \( \mathbf{v} \) is (3, 1, 8).