C

To find the angle between the vectors \( \mathbf{a} \) and \( \mathbf{b} \), we can use the formula:
\[ \cos \theta = \frac{\mathbf{a} \cdot \mathbf{b}}{\| a \| \| b \|} \]
Step 1: Calculate the dot product \( \mathbf{a} \cdot \mathbf{b} \):
\[ \mathbf{a} \cdot \mathbf{b} = (2)(3) + (3)(4) + (4)(5) = 6 + 12 + 20 = 38 \]
Step 2: Calculate the magnitudes of \( \mathbf{a} \) and \( \mathbf{b} \):
\[ \| a \| = \sqrt{(2^2 + 3^2 + 4^2)} = \sqrt{4 + 9 + 16} = \sqrt{29} \]
\[ \| b \| = \sqrt{(3^2 + 4^2 + 5^2)} = \sqrt{9 + 16 + 25} = \sqrt{50} \]
Step 3: Substitute into the formula:
\[ \cos \theta = \frac{38}{\sqrt{29} \cdot \sqrt{50}}
= \frac{38}{\sqrt{1450}}
= \frac{38}{38.07886552931954} \approx 0.9996
\] Step 4: Calculate \( \theta \):
\[ \theta = \cos^{-1}(0.9996) \approx 3.2^\circ
\] Therefore, the angle between them is approximately \( 3.2^\circ \).
Thus, the correct answer is option C.