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:
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:
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Remember the formula for the reflection of a point across a line in 3D: it involves the directional cosines of the line.
Updated On: Mar 24, 2025
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The Correct Option is D
Solution and Explanation
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, \( a + \beta + \gamma = 12 \).
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, \( a + \beta + \gamma = 12 \).
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