First slide

Direction ratios and direction cosines

Question

Triangle formed by three lines whose direction ratios are $〈- 1, 1, 1〉, 〈1, \sqrt{2}, 0〉, 〈1, 1, 0〉$ is

Moderate

A

Acute angled triangle
B

Obtuse angled triangle
C

right angled triangle
D

coincident lines

Solution

Suppose that the given lines form a triangle $A B C$
Hence,
$\begin{matrix} \cos A = \frac{- 1 + \sqrt{2}}{\sqrt{1 + 1 + 1} \sqrt{1 + 2}} = \frac{\sqrt{2} - 1}{3} \\ \cos B = \frac{1 + \sqrt{2}}{\sqrt{1 + 2} \sqrt{1 + 1}} = \frac{\sqrt{2} + 1}{\sqrt{6}} \\ \cos C = \frac{- 1 + 1}{\sqrt{1 + 1} \sqrt{1 + 1 + 1}} = 0 \end{matrix}$
Since $\cos C = 0$ ,the measure one angle in the triangle is right angle, so that the triangle formed by the given lines is right angled triangle.

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