If a line makes angles , , with the co-ordinate axes, then - Vidyadip

MCQ

If a line makes angles $\alpha, \beta, \gamma$ with the co-ordinate axes, then

A
$\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma-1=0$
B
$\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma-2=0$
✓
$\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma+1=0$
D
$\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma+2=0$

✓

Answer

Correct option: C.

$\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma+1=0$

(C) $\cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma=1$
$\begin{array}{l}\Rightarrow \frac{1+\cos 2 \alpha}{2}+\frac{1+\cos 2 \beta}{2}+\frac{1+\cos 2 \gamma}{2}=1 \\ \Rightarrow \cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma+3=2 \\ \Rightarrow \cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma+1=0\end{array}$

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