Question

The equation of the straight line making angles ${60}^o,{60}^o$ and ${45}^o$ with positive direction of the coordinate axes and passing through the point $(2,1,-1)$ is :

• A. $\sqrt{2}(x-2)=\sqrt{2}(y-1)=(z+1)$
• B. $(x-2)=\sqrt{2}(y-1)=(z+1)$
• C. $\sqrt{2}(x-2)=(y-1)=(z+1)$
• D. $(x-2)=\sqrt{(}y-1)=\sqrt{2}(z+1)$
• E. $\sqrt{2}(x-2)=(y-1)=\sqrt{2}(z+1)$

Answer 1

The correct option is A $\sqrt{2}(x-2)=\sqrt{2}(y-1)=(z+1)$

Equation of line passing through $(2,1,-1)$ and making an angles of ${60}^o,{60}^o$ and ${45}^o$ is
$\frac{x-2}{\cos {60}^o}=\frac{y-1}{\cos {60}^o}=\frac{z+1}{\cos {45}^o}$
$\Rightarrow \frac{x-2}{1/2}=\frac{y-1}{1/2}=\frac{z+1}{1/\sqrt{2}}$
$\Rightarrow \sqrt{2}(x-2)=\sqrt{2}(y-1)=z+1$