JEE Main 2014 · 6 Apr · Shift 1 · Mathematics Q84

MathematicsSingle correct+4 / -1Question 84 of 90

The angle between the lines whose direction cosines satisfy the equations $l+m+n=0$ and $l^2=m^2+n^2$ is :

\dfrac\pi6

\dfrac\pi2

\dfrac\pi3

\dfrac\pi4

Answer and worked solution

Official answer: C

Put $n=-(l+m)$ into $l^2=m^2+n^2$ : $2m^2+2lm=0$ , so $m=0$ or $m=-l$ .

The two directions are $(1,0,-1)$ and $(1,-1,0)$ . Then $\cos\theta=\dfrac{1}{\sqrt2\sqrt2}=\dfrac12$ , so $\theta=\dfrac\pi3$ .

JEE Main 2014 · 6 Apr · Shift 1, Mathematics question 84