Area of a rectangle having vertices A, B, C and D with position vectors `- hat i+1/2 hat j+4 hat k , hat i+1/2 hat j+4 hat k , hat i-1/2 hat j+4 hat k`and `- hat i-1/2 hat j+4 hat k`respectively is(A) 1/2 (B) 1 (C) 2 (D) 4

Explanation

To find the area of the rectangle with vertices A, B, C, and D given their position vectors, we will follow these steps:

### Step 1: Identify the position vectors
The position vectors of the vertices are given as:
- A: \(-\hat{i} + \frac{1}{2}\hat{j} + 4\hat{k}\)
- B: \(\hat{i} + \frac{1}{2}\hat{j} + 4\hat{k}\)
- C: \(\hat{i} - \frac{1}{2}\hat{j} + 4\hat{k}\)
- D: \(-\hat{i} - \frac{1}{2}\hat{j} + 4\hat{k}\)
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