Triangle formed by three lines whose direction ratios are −1,1,1,1,2,0,1,1,0 is - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

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.

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

Solution:

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