Direction - ratios of vector `vec(a)=hat(i)+hat(j)-2hat(k)` are :

Options

A. `lt 1, 2, 2gt`
B. `lt 1,1,-2gt`
C. `lt (2)/(sqrt(16)),(1)/(sqrt(6)),(2)/(sqrt(6))gt`
D. `lt(1)/(sqrt(6)),(1)/(sqrt(6)),(-2)/(sqrt(6))gt`

Answer

To find the direction ratios of the vector \(\vec{a} = \hat{i} + \hat{j} - 2\hat{k}\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Components of the Vector**:
The vector \(\vec{a}\) can be expressed in terms of its components along the x, y, and z axes:
\[ \vec{a} = 1\hat{i} + 1\hat{j} - 2\hat{k} \]
Here, the coefficients of \(\hat{i}\), \(\hat{j}\), and \(\hat{k}\) represent the components of the vector.

2. **Extract the Direction Ratios**:
The direction ratios of a vector are simply the coefficients of \(\hat{i}\), \(\hat{j}\), and \(\hat{k}\). From the expression above, we can identify:
- The coefficient of \(\hat{i}\) (x-component) is \(1\).
- The coefficient of \(\hat{j}\) (y-component) is \(1\).
- The coefficient of \(\hat{k}\) (z-component) is \(-2\).

3. **Write the Direction Ratios**:
Therefore, the direction ratios of the vector \(\vec{a}\) are:
\[ \text{Direction Ratios} = (1, 1, -2) \]

### Final Answer:
The direction ratios of the vector \(\vec{a} = \hat{i} + \hat{j} - 2\hat{k}\) are \(1, 1, -2\).

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