Write the direction ratios of the vector ` veca= hat i+ hat j-2 hat k`and hence calculate its direction cosines.

Explanation

To solve the problem step by step, we will first find the direction ratios of the vector \( \vec{a} = \hat{i} + \hat{j} - 2\hat{k} \) and then calculate its direction cosines.

### Step 1: Identify the components of the vector
The vector \( \vec{a} \) can be expressed in terms of its components:
- Coefficient of \( \hat{i} \) (x-component) = 1
- Coefficient of \( \hat{j} \) (y-component) = 1
- Coefficient of \( \hat{k} \) (z-component) = -2

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