COMEDK · Maths · 34. Three Dimensional Geometry
The foot of the perpendicular from \((2,4,-1)\) to the line \(x+5=\dfrac{1}{4}(y+3)=-\dfrac{1}{9}(z-6)\) is
- A \((-4,-1,-3)\)
- B \((-4,1,-3)\)
- C \((4,-1,-3)\)
- D \((-4,-1,3)\)
Answer & Solution
Correct Answer
(B) \((-4,1,-3)\)
Step-by-step Solution
Detailed explanation
The given line is \(x+5 = \dfrac{y+3}{4} = \dfrac{z-6}{-9} = \lambda\). Any point on the line is \(P(\lambda - 5, 4\lambda - 3, -9\lambda + 6)\). Let \(A = (2, 4, -1)\). The direction vector of the line is \(\vec{v} = (1, 4, -9)\). The vector…
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