8. Evaluate each exercise. a. If \( \vec{u}=(3,-5) \), find \( 4 \vec{u} \). b. If \( \vec{v}=(-4,11) \), find \( -3 \vec{v} \). c. If \( \vec{w}=\left(\frac{4}{5},-\frac{4}{5}\right) \), find \( 10 \vec{w} \)

To solve each exercise, we can simply multiply the vector components by the corresponding scalar. For \( 4 \vec{u} \), where \( \vec{u}=(3,-5) \): \[ 4 \vec{u} = 4(3,-5) = (4 \cdot 3, 4 \cdot -5) = (12, -20) \] For \( -3 \vec{v} \), where \( \vec{v}=(-4,11) \): \[ -3 \vec{v} = -3(-4,11) = (-3 \cdot -4, -3 \cdot 11) = (12, -33) \] For \( 10 \vec{w} \), where \( \vec{w}=\left(\frac{4}{5},-\frac{4}{5}\right) \): \[ 10 \vec{w} = 10\left(\frac{4}{5},-\frac{4}{5}\right) = \left(10 \cdot \frac{4}{5}, 10 \cdot -\frac{4}{5}\right) = (8, -8) \] So, the final results are: a. \( 4 \vec{u} = (12, -20) \) b. \( -3 \vec{v} = (12, -33) \) c. \( 10 \vec{w} = (8, -8) \)