COMEDK · Maths · 34. Three Dimensional Geometry
The co-ordinate of the foot of the perpendicular from \(P(1,8,4)\) on the line joining \(R(0,-1,3)\) and \(Q(2,-3,-1)\) is
- A \(\left(\dfrac{-5}{3}, \dfrac{2}{3}, \dfrac{19}{3}\right)\)
- B \(\left(\dfrac{5}{3}, \dfrac{2}{3}, \dfrac{19}{3}\right)\)
- C \(\left(\dfrac{5}{3}, \dfrac{2}{3}, \dfrac{-19}{3}\right)\)
- D \(\left(\dfrac{-5}{3}, \dfrac{-2}{3}, \dfrac{-19}{3}\right)\)
Answer & Solution
Correct Answer
(A) \(\left(\dfrac{-5}{3}, \dfrac{2}{3}, \dfrac{19}{3}\right)\)
Step-by-step Solution
Detailed explanation
The line passes through \(R(0, -1, 3)\) and \(Q(2, -3, -1)\). The direction vector of the line is \(\vec{v} = Q - R = (2 - 0, -3 - (-1), -1 - 3) = (2, -2, -4)\). The equation of the line can be written in parametric form as \(x = 2t\), \(y = -1 - 2t\), \(z = 3 - 4t\). Let \(M\)…
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