Question:
The equation of a line passing through the point $(1,-2,3)$ and equally inclined to the axes are:
The equation of a line passing through the point $(1,-2,3)$ and equally inclined to the axes are:
Show Hint
Equally inclined $\Rightarrow$ direction ratios are equal (±1, ±1, ±1).
Updated On: Apr 30, 2026
- \(x+1 = y-2 = z+3 \)
- \(x+1 = y-2 = z-3 \)
- \(x-1 = y-2 = z+3 \)
- \(x-1 = y+2 = z+3 \)
- \(x-1 = y+2 = z-3 \)
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The Correct Option is
Solution and Explanation
Concept:
A line equally inclined to axes has direction ratios:
\[
(1,1,1) \text{ or } (-1,-1,-1)
\]
Step 1: Use symmetric form.
\[ \frac{x-1}{l} = \frac{y+2}{m} = \frac{z-3}{n} \]
Step 2: Take equal direction ratios.
\[ l=m=n=1 \] \[ \Rightarrow x-1 = y+2 = z-3 \]
Step 3: Check option form.
Matches option (E)
Step 1: Use symmetric form.
\[ \frac{x-1}{l} = \frac{y+2}{m} = \frac{z-3}{n} \]
Step 2: Take equal direction ratios.
\[ l=m=n=1 \] \[ \Rightarrow x-1 = y+2 = z-3 \]
Step 3: Check option form.
Matches option (E)
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