Question

If a vector make angles $\alpha ,\beta$ and $\gamma$ with axes $x,y$ and $z$ , then $\cos 2\alpha +\cos 2\beta +\cos 2\gamma =$

• A. $0$
• B. $-1$
• C. $\frac{1}{2}$
• D. $2$

Answer 1

The correct option is B $-1$

$\alpha ,\beta ,\gamma \to cosineswithx,y,zaxisThen\cos 2\alpha +\cos 2\beta +\cos 2\gamma =?WeKnow=\cos 2Q=2\cos {}^{2}Q-1=\cos 2\alpha +\cos 2\beta +\cos 2\gamma =2\cos {}^2\alpha -1+2\cos {}^2\beta -1+2\cos {}^2\gamma -1=2(\cos {}^2\alpha +\cos {}^2\beta +\cos {}^2\gamma )-3=[[\cos {}^2\alpha +\cos {}^2\beta +\cos {}^2\gamma ]=1]=2\left(1\right)-3=-1OPTION:B$