First slide

Direction ratios and direction cosines

Question

The direction cosines of the line passing through $P (1, 2, 5)$ and $Q (2, 4, 7)$ are

Easy

A

$(\frac{1}{3}, \frac{- 2}{3}, \frac{2}{3})$
B

$(\frac{1}{3}, \frac{2}{3}, \frac{2}{3})$
C

$(\frac{1}{3}, \frac{2}{3}, \frac{- 2}{3})$
D

$(\frac{- 1}{3}, \frac{2}{3}, \frac{- 2}{3})$

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 $P (1, 2, 5), Q (2, 4, 7)$ is $〈1, 2, 2〉$
Direction cosines are $〈\frac{1}{\sqrt{1 + 4 + 4}}, \frac{2}{\sqrt{1 + 4 + 4}}, \frac{2}{\sqrt{1 + 4 + 4}}〉 = 〈\frac{1}{3}, \frac{2}{3}, \frac{2}{3}〉$

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