(D) The coordinates of point $P$ are $(x, y, z) = (3, 12, 4)$.The distance $OP$ from the origin $(0, 0, 0)$ is given by $r = \sqrt{x^2 + y^2 + z^2}$.$

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$\frac{3}{13}, \frac{12}{13}, \frac{4}{13}$

(D) The coordinates of point $P$ are $(x, y, z) = (3, 12, 4)$.The distance $OP$ from the origin $(0, 0, 0)$ is given by $r = \sqrt{x^2 + y^2 + z^2}$.$r = \sqrt{3^2 + 12^2 + 4^2} = \sqrt{9 + 144 + 16} = \sqrt{169} = 13$.The direction cosines $(l, m, n)$ are given by $\frac{x}{r}, \frac{y}{r}, \frac{z}{r}$.$l = \frac{3}{13}$,$m = \frac{12}{13}$,$n = \frac{4}{13}$.Thus,the direction cosines are $\frac{3}{13}, \frac{12}{13}, \frac{4}{13}$.

Class 12 Mathematics THREE DIMENSIONAL GEOMETRY System of co-ordinates, Direction cosines and direction ratios, Projection

Easy

The coordinates of a point $P$ are $(3, 12, 4)$ with respect to origin $O$. Find the direction cosines of $OP$.

A
$3, 12, 4$
B
$\frac{1}{4}, \frac{1}{3}, \frac{1}{2}$
C
$\frac{3}{\sqrt{13}}, \frac{1}{\sqrt{13}}, \frac{2}{\sqrt{13}}$
D
$\frac{3}{13}, \frac{12}{13}, \frac{4}{13}$

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THREE DIMENSIONAL GEOMETRY

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System of co-ordinates, Direction cosines and direction ratios, Projection

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The coordinates of a point $P$ are $(3, 12, 4)$ with respect to origin $O$. Find the direction cosines of $OP$.

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