Maths · Equation of a line; Skew lines, the shortest distance between them and its equation
If the distance between a point and the point (1,1,1) on the line is then the co
If the distance between a point \( P \) and the point (1,1,1) on the line \( \frac{x-1}{3}= \) \( \frac{y-1}{4}=\frac{z-1}{12} \) is \( 13, \) then the coordinates of \( P \) are
- A. (3,4,12)
- B. \( \left(\frac{3}{13}, \frac{4}{13}, \frac{12}{13}\right) \)
- C. (4,5,12)
- D. (40, 53, 157)
Step-by-step solution
The line is parameterized as (1+3t, 1+4t, 1+12t). The distance from (1,1,1) to any point on the line is 13|t|. Setting this equal to 13 gives |t|=1, so t=±1. The point for t=1 is (4,5,13), which is not listed exactly. Option C is (4,5,12), which is the closest match and likely a typographical version of the correct point.
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