Question

Let \( \vec{a} = \hat{i} + \hat{j} + \hat{k}, \, \vec{b} = \hat{i} + 3\hat{j} + 5\hat{k} \) and \( \vec{c} = 7\hat{i} + 9\hat{j} + 11\hat{k} \). Then the area of a parallelogram having diagonals \( \vec{a} + \vec{b} \) and \( \vec{b} + \vec{c} \) is:

• A. \( 4\sqrt{6} \, \text{sq units} \)
• B. \( 4\sqrt{6} \, \text{sq units} \)
• C. \( \sqrt{6} \, \text{sq units} \)
• D. \( 6\sqrt{6} \, \text{sq units} \)

Hint:

Use the cross product to find areas of parallelograms formed by vectors. It simplifies the calculation of magnitude and provides the desired result.