Vector Basics

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A unit vector in the direction of î + ĵ + k̂ is

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1. **Definition**: A unit vector $\hat{u}$ in the direction of $\vec{a}$ is defined as $\frac{\vec{a}}{|\vec{a}|}$.
2. **Calculate Magnitude**: $|\hat{i} + \hat{j} + \hat{k}| = \sqrt{1^2 + 1^2 + 1^2} = \sqrt{3}$.
3. **Construct Unit Vector**:
   - $\hat{u} = \frac{1}{\sqrt{3}} (\hat{i} + \hat{j} + \hat{k})$.
4. **Verification**: The magnitude of this resulting vector is exactly 1.

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