Question

The sum of the squares of sine of the angles made by the line $AB$ with $OX,OY,OZ$ where $O$ is the origin is

• A. $1$
• B. $2$
• C. $-1$
• D. $3$

Answer 1

Answer: (B)

$2$

Let $\cos \alpha ,\cos \beta$ and $\cos \gamma$ be the direction cosines.
We know that ${\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma =1$
Now rewrite it as ${\cos }^2\alpha =1-{\sin }^2\alpha$
$\Rightarrow {\cos }^2\beta =1-{\sin }^2\beta$
$\Rightarrow {\cos }^2\gamma =1-{\sin }^2\gamma$
Then we get, ${\sin }^2\alpha +{\sin }^2\beta +{\sin }^2\gamma =2$