Write the direction ratio's of the vector `vec a=4hati-2hatj+hatk` and hence calculate its direction cosines.

Explanation

To solve the problem of finding the direction ratios and direction cosines of the vector \(\vec{a} = 4\hat{i} - 2\hat{j} + \hat{k}\), we will follow these steps:

### Step 1: Identify the coefficients of the vector
The vector \(\vec{a}\) is given as:
\[ \vec{a} = 4\hat{i} - 2\hat{j} + \hat{k} \]
From this, we can identify the coefficients:
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