Find a unit vector `vecc` if `-hati+hatj-hatk` bisects the angle between vectors `vecc` and `3hati+4hatj`.

Explanation

To find the unit vector \(\vec{c}\) that bisects the angle between the vectors \(\vec{c}\) and \(\vec{b} = 3\hat{i} + 4\hat{j}\), given that the vector \(-\hat{i} + \hat{j} - \hat{k}\) bisects the angle between these two vectors, we can follow these steps:

### Step 1: Define the vectors
Let:
- \(\vec{a} = -\hat{i} + \hat{j} - \hat{k}\)
- \(\vec{b} = 3\hat{i} + 4\hat{j}\)
- \(\vec{c}\) be the unit vector we need to find.

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