Find an equation of the line segment joining the given pair of points. \( (-5,-8,6) \) and \( (-4,8,-8) \) Choose the correct answer below. A. \( \langle x, y, z\rangle=t\langle 1,16,-14\rangle \), for \( -\infty

To find the equation of the line segment joining the points \((-5,-8,6)\) and \((-4,8,-8)\), we can use the parametric form of the line segment. 1. **Find the direction vector**: The direction vector \(\mathbf{d}\) from point \(A(-5,-8,6)\) to point \(B(-4,8,-8)\) is calculated as follows: \[ \mathbf{d} = B - A = (-4, 8, -8) - (-5, -8, 6) = (1, 16, -14) \] 2. **Parametric equation of the line segment**: The parametric equation of the line segment can be expressed as: \[ \langle x, y, z \rangle = A + t\mathbf{d} \] where \(A\) is the starting point, \(\mathbf{d}\) is the direction vector, and \(t\) varies from \(0\) to \(1\) to represent the segment from \(A\) to \(B\). Substituting \(A\) and \(\mathbf{d}\): \[ \langle x, y, z \rangle = \langle -5, -8, 6 \rangle + t\langle 1, 16, -14 \rangle \] This gives us: \[ \langle x, y, z \rangle = \langle -5 + t, -8 + 16t, 6 - 14t \rangle \] for \(0 \leq t \leq 1\). 3. **Choose the correct answer**: The correct answer that matches this form is: \[ \langle x, y, z \rangle = \langle -5, -8, 6 \rangle + t\langle 1, 16, -14 \rangle, \text{ for } 0 \leq t \leq 1 \] Thus, the correct answer is: **B.** \( \langle x, y, z\rangle=\langle-5,-8,6\rangle+t\langle 1,16,-14\rangle \), for \( 0 \leq t \leq 1 \)