Answer to Question #118532 in Analytic Geometry for Joshua

Question

Suppose that the coordinates of R be (3,4,12), what are the direction cosines of
(OR) ƒ—?
a.\\(\\frac{3}{14}, \\frac{4}{14}, \\frac{12}{14}\\)
b.\\(\\frac{1}{13}, \\frac{4}{13}, \\frac{11}{13}\\)
c.\\(\\frac{1}{14}, \\frac{4}{14}, \\frac{11}{14}\\)
d.\\(\\frac{3}{13}, \\frac{4}{13}, \\frac{12}{13}\\)

Answer 1

Given co-ordinate of R is $(3,4,12)$ .

Hence the direction ratio's of OR is $(3,4,12)$ .

Now, $|OR| = \sqrt{3^2+4^2+12^2} = \sqrt{169} = 13$ .

Hence the direction cosine of OR is $\frac{OR}{|OR|} = \frac{(3,4,12)}{13} = (\frac{3}{13}, \frac{4}{13}, \frac{12}{13})$ .

Correct option is option d.