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## Q. 3.4

Find the unit tangent vector to the curve $\mathbf{f}=(\ln t) \mathbf{i}+(1 / t) \mathbf{j}$ at t = 1.

## Verified Solution

$\mathbf{f}^{\prime}(t)=(1 / t) \mathbf{i}-\left(1 / t^{2}\right) \mathbf{j}=\mathbf{i}-\mathbf{j}$ when t = 1. Since $\left|\mathbf{f}^{\prime}\right|=|\mathbf{i}-\mathbf{j}|=\sqrt{2}$ we find that,
$\mathbf{T}=\frac{\mathbf{1}}{\sqrt{2}} \mathbf{i}-\frac{1}{\sqrt{2}} \mathbf{j}$.