Question

The centroid of a triangle formed by the points $(0,0),(\cos \theta ,\sin \theta )$ and $(\sin \theta -\cos \theta )$ lies on the line $y=2x$ then $\theta =$

• A. ${\tan }^{-1}2$
• B. ${\tan }^{-1}3$
• C. ${\tan }^{-1}(-3)$
• D. ${\tan }^{-1}(-2)$

Answer 1

The correct option is C ${\tan }^{-1}(-3)$

Given Cordinates of triangle are $(0,0),(cos\theta ,sin\theta ),(sin\theta ,-cos\theta )$

Centroid of triangle is given by=$\frac{0+cos\theta +sin\theta }{3},\frac{sin\theta -cos\theta }{3}$

Since the Centroisd lies on the plane y=2x

$\therefore \frac{sin\theta -cos\theta }{3}=2\frac{sin\theta +cos\theta }{3}$

$\to sin\theta -cos\theta =2sin\theta +2cos\theta$

$\to sin\theta =-3cos\theta$

$\to tan\theta =-3$

$\to \theta =ta{n}^{-1}(-3)$