Let \( \mathbf{v}=-15 \mathbf{i}+8 \mathbf{j} \), find \( \|\mathbf{v}\| \)

To find the magnitude of the vector \( \mathbf{v} = -15 \mathbf{i} + 8 \mathbf{j} \), we use the formula for the magnitude of a vector in two dimensions: \[ \|\mathbf{v}\| = \sqrt{(-15)^2 + (8)^2} \] Calculating the squares: \[ (-15)^2 = 225 \quad \text{and} \quad (8)^2 = 64 \] Adding these results together: \[ \|\mathbf{v}\| = \sqrt{225 + 64} = \sqrt{289} \] Finally, taking the square root gives: \[ \|\mathbf{v}\| = 17 \] So, the magnitude of the vector \( \mathbf{v} \) is \( 17 \).