vector basics

Question

The magnitude of vector 3î + 4ĵ is

RankGuru · Accepted Answer

1. **Definition of Magnitude**: For a vector $\vec{v} = a\hat{i} + b\hat{j}$, the magnitude (length) is $|\vec{v}| = \sqrt{a^2 + b^2}$.
2. **Identify Components**: $a = 3, b = 4$.
3. **Calculation**:
   - $|\vec{v}| = \sqrt{3^2 + 4^2}$
   - $|\vec{v}| = \sqrt{9 + 16} = \sqrt{25}$
4. **Result**: The magnitude is **5**.

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