If the centroid of the triangle formed by the points (0, 0), $\left( {\cos {\rm{\theta }},\sin {\rm{\theta }}} \right)$ and $\left( {\sin {\rm{\theta }},\; - \cos {\rm{\theta }}} \right)$ lies on the line $y = 2x$, then ${\rm{\theta }}$ is equal to

${\tan ^{ - 1}}\left( { - 2} \right)$

JEE MATHEMATICS MCQ: 3D GEOMETRY SYSTEM

1 Easy

1 of 1

Application +4 | -1

If the centroid of the triangle formed by the points (0, 0),

\left( {\cos \mathrm{\theta },\sin \mathrm{\theta }} \right)

and

\left( {\sin \mathrm{\theta },\; - \cos \mathrm{\theta }} \right)

lies on the line

y = 2x

, then

\mathrm{\theta }

is equal to

View answer and explanation

Correct option: C

{\tan ^{ - 1}}\left( { - 3} \right)

Option C (

{\tan ^{ - 1}}\left( { - 3} \right)

) is correct because the centroid coordinates satisfy the equation of the line y = 2x, leading to the solution

\tan{\theta} = -3

Practice All Chapter MCQs →

\left( { - 10,\;8} \right)

\left( { - 6,\;12} \right)

\left( {4,\; - 2} \right)

\left( { - 2,\;4} \right)

y z

(1,-2,4)

(3,-4

5)

p

2 x+y-3=0

3 x-y-2=0

x-p y+5=0

O\left( {0,0} \right),A\left( {a,0} \right)

B\left( {0,a} \right).

A(1,0,3)

B(4,7,1)

C(3,5,3)

\frac{x}{1}=\frac{y}{2}=\frac{z}{3}, \frac{x}{2}=\frac{y}{1}=\frac{z}{3}

\frac{x-1}{1}=\frac{2-y}{2}, z=3