First slide

Direction ratios and direction cosines

Question

The direction cosines of the line passing through $P (- 2, 4, 3)$ and the origin are

Easy

A

$(\frac{- 2}{\sqrt{29}}, \frac{4}{\sqrt{29}}, \frac{3}{\sqrt{29}})$
B

$(\frac{- 2}{\sqrt{29}}, \frac{- 4}{\sqrt{29}}, \frac{3}{\sqrt{29}})$
C

$(\frac{- 2}{\sqrt{29}}, \frac{- 4}{\sqrt{29}}, \frac{- 3}{\sqrt{29}})$
D

$(\frac{- 2}{\sqrt{29}}, \frac{4}{\sqrt{29}}, \frac{- 3}{\sqrt{29}})$

Solution

The direction ratios of the line joining the points $A (x_{1}, y_{1}, z_{1})$ and $B (x_{1}, y_{1}, z_{1})$ is $〈x_{2} - x_{1}, y_{2} - y_{1}, z_{2} - z_{1}〉$
The direction ratios of the line joining the points $P (- 2, 4, 3), Q (0, 0, 0)$ is $〈- 2, 4, 3〉$
Direction cosines are $〈- \frac{2}{\sqrt{4 + 16 + 9}}, \frac{4}{\sqrt{4 + 16 + 9}}, \frac{3}{\sqrt{4 + 16 + 9}}〉 = 〈- \frac{2}{\sqrt{29}}, \frac{4}{\sqrt{29}}, \frac{3}{\sqrt{29}}〉$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App