Answer to Question #120969 in Analytic Geometry for Samson

Question

Suppose that the coordinates of R be (3,4,12), what are the direction cosines of
(
O
R
)
(OR) ƒ—?

Answer 1

$\overrightarrow{OR}=(3-0)\hat{i}+(4-0)\hat{j}+(12-0)\hat{k}=$ $3\hat{i}+4\hat{j}+12\hat{k}$

$|\overrightarrow{OR}|=\sqrt{3^2+4^2+12^2}=13$

Unit vector $=\frac{3}{13}\hat{i}+\frac{4}{13}\hat{j}+\frac{12}{13}\hat{k}$

Direction cosines $\equiv (\frac{3}{13},\frac{4}{13},\frac{12}{13})$