Question

The line $x+2y-z-3=0,x+3y-z-4=0$ is parallel to

• A. xy-plane
• B. ys-plane
• C. zx-plane
• D. z-axis

Answer 1

The correct option is C zx-plane

Let line has $DRs\Rightarrow (a,b,c)$

$a+2b-c=0---\left(1\right)$

$a+3b-c=0----\left(2\right)$

$\left(2\right)-\left(1\right)$

$=\Rightarrow b=0\Rightarrow a-c=0$

$\therefore DRd$ of the line are $(a,o,a)$ or $(1,0,1)$

$\Rightarrow DCx$ are $(\frac{1}{\sqrt{2}},0,\frac{1}{\sqrt{2}})$

$(\frac{1}{\sqrt{2}},0,\frac{1}{\sqrt{2}})\equiv (\cos \alpha ,\cos \beta ,\cos \gamma )$

$\Rightarrow \beta =90$

$\Rightarrow$ line is $\perp$ to $y$ axis

$\Rightarrow$ line is parallel to $x-2$ plane