First slide

Direction ratios and direction cosines

Question

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

Moderate

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

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

Solution

Required direction cosines are
$\begin{array}{l} \frac{3}{\sqrt{3^{2} + 12^{2} + 4^{2}}}, \frac{12}{\sqrt{3^{2} + 12^{2} + 4^{2}}}, \frac{4}{\sqrt{3^{2} + 12^{2} + 4^{2}}} \\ i.e., \frac{3}{13}, \frac{12}{13}, \frac{4}{13} \end{array}$

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