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Question

In the following cases, find the coordinates of the foot of the perpendicular drawn from the origin.
2x+3y+4z12=0

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Solution

Direction ratio of any line normal to
2x+3y+4z12=0 is (2,3,4)
Equation of line through (O,O,O) and is to given lines is
x0(2)=y0=z44
any point on the lines is (2λ,3λ,4λ) but this lines on the given plane
2(2λ)+3(3λ)+4(4λ)12=0λ=1229
Food of is (2×1229,3×1229,4×1229)
=(2429,3629,4829).

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