WBJEE · Maths · Three Dimensional Geometry
A point \(P\) lies on a line through \(Q(1,-2,3)\) and is parallel to the line \(\frac{x}{1}=\frac{y}{4}=\frac{z}{5},\) If \(P\) lies on the plane \(2 x+3 y-4 z+22=0,\) then segment PQ equals
- A \(\sqrt{42}\) units
- B \(\sqrt{32}\) units
- C 4 units
- D 5 units
Answer & Solution
Correct Answer
(A) \(\sqrt{42}\) units
Step-by-step Solution
Detailed explanation
Equation of line through \(Q(1,-2,3)\) and parallel to the line \(\frac{x}{1}=\frac{y}{4}=\frac{z}{5}\) is \(\frac{x-1}{1}=\frac{y+2}{4}=\frac{z-3}{5}=\lambda \quad\) (say) since, point \(P\) lies on above line. \(\therefore\) \[ P(\lambda+1,4 \lambda-2,5 \lambda+3) \] since,…
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