The coordinates of a point P are(3, 12, 4) w.r.t origin O, then the direction cosines of OP are

Question

The coordinates of a point P are(3, 12, 4) w.r.t origin O, then the direction cosines of OP are (A) 3, 12, 4 (B) (1/4),(1/3),(1/2) (C) (3/√13),(1/√13),(2/√13) (D) (3/13),(12/13),(4/13)

Tardigrade Admin · Accepted Answer

D.r's of OP are (3, 12, 4) also √ 32 + 122 + 42 = 13 D,c's are ( (3/13),(12/13),(4/13) )

Q. The coordinates of a point P are(3, 12, 4) w.r.t origin O, then the direction cosines of OP are

3, 12, 4

$\frac{1}{4}, \frac{1}{3}, \frac{1}{2}$

$\frac{3}{13}, \frac{1}{13}, \frac{2}{13}$

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

D.r's of OP are (3, 12, 4)
also $3^{2} + 1 2^{2} + 4^{2} = 13$
D,c's are $(\frac{3}{13}, \frac{12}{13}, \frac{4}{13})$

Q. The coordinates of a point P are(3, 12, 4) w.r.t origin O, then the direction cosines of OP are

3, 12, 4

41​,31​,21​

13​3​,13​1​,13​2​

133​,1312​,134​

D.r's of OP are (3, 12, 4) also 32+122+42​=13 D,c's are (133​,1312​,134​)

$\frac{1}{4}, \frac{1}{3}, \frac{1}{2}$

$\frac{3}{13}, \frac{1}{13}, \frac{2}{13}$

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

D.r's of OP are (3, 12, 4)
also $3^{2} + 1 2^{2} + 4^{2} = 13$
D,c's are $(\frac{3}{13}, \frac{12}{13}, \frac{4}{13})$