Question

If the image of the point \( (4, 4, 3) \) in the line \( \frac{x-1}{2} = \frac{y-2}{1} = \frac{z-1}{3} \) is \( (a, \beta, \gamma) \), then \( a + \beta + \gamma \) is equal to:

• A. 9
• B. 7
• C. 8
• D. 12

Hint:

Remember the formula for the reflection of a point across a line in 3D: it involves the directional cosines of the line.

Answer 1

The Correct Option is D

Step 1: Find the image point.
Use the formula for the image of a point about a line in 3D geometry to calculate \( (a, \beta, \gamma) \).
Step 2: Calculate the sum.
\( a + \beta + \gamma = 12 \).
Conclusion:
Thus, \( a + \beta + \gamma = 12 \).