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Please solve RD Sharma class 12 chapter The Plane exercise 28.15 question 13 maths textbook solution

Answers (1)

Answer: \frac{12}{29}, \frac{-18}{29}, \frac{24}{29}

Hint:

Let cosines be L,M,N.

\vec{r} \cdot \hat{n}=d .

Given:

Find the coordinates of the foot of the perpendicular drawn from the origin to the plane 2x-3y+4z-6=0

Solution:

2x-3y+4z-6=0

\begin{aligned} &2 x-3 y+4 z=6 \\\\ &\sqrt{2^{2}+3^{2}+4^{2}}=\sqrt{29} \\\\ &=\frac{2}{\sqrt{29}} x-\frac{3}{\sqrt{29}} y+\frac{4}{\sqrt{29}} 3 \\\\ &=\frac{6}{\sqrt{29}} \end{aligned}

Direction cosines =\frac{2}{\sqrt{29}}, \frac{-3}{\sqrt{4}},+\frac{4}{\sqrt{29}}

 

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