Question

$\overrightarrow{A}$ is a vector with direction cosines $\cos \alpha$, $\cos \beta$ and $\cos \gamma$. Assuming the $y-z$ plane as a mirror, the direction cosines of the reflected image of $\overrightarrow{A}$ in the $y-z$ plane are

• A. $\cos \alpha ,\cos \beta ,\cos \gamma$
• B. $\cos \alpha ,-\cos \beta ,\cos \gamma$
• C. $-\cos \alpha ,\cos \beta ,\cos \gamma$
• D. $-\cos \alpha ,-\cos \beta ,-\cos \gamma$

Answer 1

The correct option is C $-\cos \alpha ,\cos \beta ,\cos \gamma$

The directional cosines of $A$ are $\cos \alpha ,\cos \beta ,\cos \gamma$

Given that $y-z$ plane is mirror

Only $x$ coordinate of $A$ will change and $y,z$ coordinates will remain same because the point is reflected about $y-z$ plane

On $y-z$ plane $x=0$ , so the directional cosine of reflected point in $x$ direction is $-\cos \alpha$

Therefore the directional cosines of reflected image is $-\cos \alpha ,\cos \beta ,\cos \gamma$