Question

The foot of the perpendicular drawn from the point \((1,8,4)\) on the line joining the points \((0,-11,4)\) and \((2,-3,1)\) is
(A) \((4,5,2)\)
(B) \((-4,5,2)\)
(C) \((4,-5,2)\)
(D) \((4,5,-2)\)

Answer 1

Ans: (D)
Hint: Equation of line is
$$
\frac{x}{9}=\frac{y+11}{8}=\frac{z-4}{-3}
$$
Let foot of \(\perp\) be \(P(2 \lambda, 8 \lambda-11,-3 \lambda+4)\) DR's of line joining \((1,8,4)\) and ' \(P\) ' is
\((2 \lambda-1,8 \lambda-19,-3 \lambda)\)
\(\therefore 2(2 \lambda-1)+8(8 \lambda-19)-3(-3 \lambda)=0\)
\(\Rightarrow 4 \lambda+64 \lambda+9 \lambda=2+152\)
\(\Rightarrow 77 \lambda=154 \quad \Rightarrow \lambda=2\)
\(\therefore\) ' \(P\) ' is \((4,5,-2)\)

Answer 2

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Answer 3

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