Find two vectors parallel to \( \mathbf{v} \) of the given length. \[ v=\langle 9,-12,0\rangle \text {; length }=20 \] The vector in the direction of \( \mathbf{v} \) is \( \langle\square, \square, \square \).

To find two vectors parallel to \( \mathbf{v} = \langle 9, -12, 0 \rangle \) with a length of 20, follow these steps: 1. **Calculate the Length of \( \mathbf{v} \):** \[ \|\mathbf{v}\| = \sqrt{9^2 + (-12)^2 + 0^2} = \sqrt{81 + 144 + 0} = \sqrt{225} = 15 \] 2. **Find the Unit Vector in the Direction of \( \mathbf{v} \):** A unit vector \( \mathbf{u} \) in the direction of \( \mathbf{v} \) is obtained by dividing each component of \( \mathbf{v} \) by its length: \[ \mathbf{u} = \left\langle \frac{9}{15}, \frac{-12}{15}, \frac{0}{15} \right\rangle = \left\langle \frac{3}{5}, \frac{-4}{5}, 0 \right\rangle \] 3. **Scale the Unit Vector to the Desired Length (20):** Multiply the unit vector \( \mathbf{u} \) by 20 to get a vector in the same direction with length 20: \[ \mathbf{w}_1 = 20 \times \mathbf{u} = 20 \times \left\langle \frac{3}{5}, \frac{-4}{5}, 0 \right\rangle = \left\langle 12, -16, 0 \right\rangle \] 4. **Find the Opposite Vector:** The opposite vector \( \mathbf{w}_2 \) will also be parallel to \( \mathbf{v} \) but points in the opposite direction: \[ \mathbf{w}_2 = -\mathbf{w}_1 = \left\langle -12, 16, 0 \right\rangle \] **Final Answer:** Two vectors parallel to \( \mathbf{v} \) with length 20 are \[ \boxed{ \left\langle 12,\ -16,\ 0 \right\rangle \quad \text{and} \quad \left\langle -12,\ 16,\ 0 \right\rangle } \]