Question:medium
If the distances of the point \( (1,2,a) \) from the line
\[
\frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1}
\]
along the lines
\[
L_1:\ \frac{x-1}{3}=\frac{y-2}{4}=\frac{z-a}{b}
\quad \text{and} \quad
L_2:\ \frac{x-1}{1}=\frac{y-2}{4}=\frac{z-a}{c}
\]
are equal, then \( a+b+c \) is equal to:
If the distances of the point \( (1,2,a) \) from the line
\[
\frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1}
\]
along the lines
\[
L_1:\ \frac{x-1}{3}=\frac{y-2}{4}=\frac{z-a}{b}
\quad \text{and} \quad
L_2:\ \frac{x-1}{1}=\frac{y-2}{4}=\frac{z-a}{c}
\]
are equal, then \( a+b+c \) is equal to:
Show Hint
When distances are measured along lines, compare ratios of direction ratios instead of using perpendicular distance formulas.
Updated On: Apr 3, 2026
- \(5\)
- \(6\)
- \(4\)
- \(7\)
Show Solution
The Correct Option is A
Solution and Explanation
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