Find the length of the vector $\vec{a} = 3\hat{i} - 4\hat{j} + 12\hat{k}$ and find its unit vector.

Question

Accepted Answer

**Step 1: Calculate the magnitude (length)**
$$|\vec{a}| = \sqrt{3^2 + (-4)^2 + 12^2} = \sqrt{9 + 16 + 144} = \sqrt{169} = 13$$

The length is **13 units**.

**Step 2: Find the unit vector $\hat{a}$**
The unit vector is given by $\hat{a} = \frac{\vec{a}}{|\vec{a}|}$:
$$\hat{a} = \frac{3\hat{i} - 4\hat{j} + 12\hat{k}}{13} = \frac{3}{13}\hat{i} - \frac{4}{13}\hat{j} + \frac{12}{13}\hat{k}$$

Find the length of the vector $\vec{a} = 3\hat{i} - 4\hat{j} + 12\hat{k}$ and find its unit vector. - DDCET Q&A

Find the length of the vector $\vec{a} = 3\hat{i} - 4\hat{j} + 12\hat{k}$ and find its unit vector.

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