Question

If \( \theta \) is the angle between the lines \( AB \) and \( AC \) where A, B, and C are the three points with coordinates \( (1, 2, -1) \), \( (2, 0, 3) \), \( (3, -1, 2) \) respectively, then \[ \sqrt{62} \cos \theta \] is equal to

• A. 20
• B. 10
• C. 30
• D. 40

Hint:

To find the cosine of the angle between two vectors, use the formula \( \cos \theta = \frac{\vec{AB} \cdot \vec{AC}}{|\vec{AB}| |\vec{AC}|} \).

Answer 1

The Correct Option is A

Step 1: Using the formula for the cosine of the angle between two vectors.
The cosine of the angle \( \theta \) between two vectors \( \vec{AB} \) and \( \vec{AC} \) is given by: \[ \cos \theta = \frac{\vec{AB} \cdot \vec{AC}}{|\vec{AB}| |\vec{AC}|} \] After calculating the dot product and magnitudes, the result is \( 20 \).

Step 2: Conclusion.
Thus, the correct answer is option (A).

Final Answer: \[ \boxed{\text{(A) } 20} \]