Question

It is known that \( AB = 2a - 6b \) and \( AC = 3a + b \), where \( a \) and \( b \) are mutually perpendicular unit vectors. Determine the angles of the AABC.

• A. \( \frac{\pi}{6} \)
• B. \( \frac{\pi}{4} \)
• C. \( \frac{\pi}{2} \)
• D. \( \pi \)

Hint:

When vectors are perpendicular, their dot product is zero, which helps in calculating the angle between them.

Answer 1

The Correct Option is C

The angle between the vectors \( AB \) and \( AC \) can be calculated using the dot product formula. Since \( a \) and \( b \) are perpendicular unit vectors, their dot product is zero. Hence, the angle between \( AB \) and \( AC \) is \( \frac{\pi}{2} \).