Question

Let \(ABCD\) be a parallelogram. If \( \vec{AB} = \hat{i} + 3\hat{j} + 7\hat{k} \), \( \vec{AD} = 2\hat{i} + 3\hat{j} - 5\hat{k} \), and \( \vec{p} \) is a unit vector parallel to \( \vec{AC} \), then \( \vec{p} \) is equal to

• A. \( \frac{1}{3}(2\hat{i}+\hat{j}+2\hat{k}) \)
• B. \( \frac{1}{3}(2\hat{i}-2\hat{j}+\hat{k}) \)
• C. \( \frac{1}{7}(3\hat{i}+6\hat{j}+2\hat{k}) \)
• D. \( \frac{1}{7}(6\hat{i}+2\hat{j}+3\hat{k}) \)
• E. \( \frac{1}{7}(6\hat{i}+2\hat{j}-3\hat{k}) \)

Hint:

Always remember: diagonal of parallelogram = sum of adjacent sides.

Answer 1

The Correct Option is C