Question

The unit vector perpendicular to the vectors \( 6i + 2j + 3k \) and \( 3i - 6j - 2k \) is:

• A. \( \frac{2i - 3j - 6k}{7} \)
• B. \( \frac{2i - 3j + 6k}{7} \)
• C. \( \frac{2i + 3j - 6k}{7} \)
• D. None of these

Hint:

The cross product of two vectors gives a vector perpendicular to both, and normalizing it gives the unit vector.

Answer 1

The Correct Option is C

Step 1: Find the cross product.
To find the unit vector perpendicular to both vectors, we first find the cross product and then normalize the resulting vector. The correct unit vector is \( \frac{2i + 3j - 6k}{7} \).
Thus, the correct answer is (3).