Find the unit vector in the same direction as the vector \( \mathbf{u}=[-7,4] \). \[ [\text { Ex: } 1.234, \text { Ex: } 1.234] \]

To find the unit vector in the same direction as the vector \( \mathbf{u}=[-7,4] \), we first need to calculate the magnitude of \( \mathbf{u} \): \[ \|\mathbf{u}\| = \sqrt{(-7)^2 + (4)^2} = \sqrt{49 + 16} = \sqrt{65} \] Next, we divide each component of \( \mathbf{u} \) by its magnitude: \[ \text{Unit vector} = \left[\frac{-7}{\sqrt{65}}, \frac{4}{\sqrt{65}}\right] \] This simplifies to: \[ \approx [-0.865, 0.494] \] So, the unit vector in the same direction as \( \mathbf{u} \) is approximately \[ [-0.865, 0.494] \]