Find the direction cosines of a line which makes equal angles with the coordinate axes.

 

 

 

 

 
 
 
 
 

Answers (1)

Let the direction cosines of the line make an angle \alpha with each of the coordinate axes and direction cosines can be l, m and n .

\therefore l=\cos \alpha ,\: m=\cos \alpha \:\: and\: \: n=\cos \alpha

l^2+m^2+n^2=1

\therefore \cos ^{2}\alpha +\cos ^{2}\alpha+\cos ^{2}\alpha=1

\Rightarrow 3\cos ^{2}\alpha=1

\Rightarrow \cos ^{2}\alpha=\frac{1}{3}

\Rightarrow \cos \alpha=\pm \frac{1}{\sqrt{3}}

Thus the direction cosines are \left ( \pm \frac{1}{\sqrt{3}},\pm \frac{1}{\sqrt{3}},\pm \frac{1}{\sqrt{3}} \right )

Preparation Products

Knockout NEET May 2021 (One Month)

An exhaustive E-learning program for the complete preparation of NEET..

₹ 14000/- ₹ 6999/-
Buy Now
Foundation 2021 Class 10th Maths

Master Maths with "Foundation course for class 10th" -AI Enabled Personalized Coaching -200+ Video lectures -Chapter-wise tests.

₹ 350/- ₹ 112/-
Buy Now
Knockout JEE Main April 2021 (One Month)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 14000/- ₹ 6999/-
Buy Now
Knockout NEET May 2021

An exhaustive E-learning program for the complete preparation of NEET..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions