Q92 / 180 · COMEDK 2024 (Memory Based) · Mathematics
The line $\frac{x-1}{2}=\frac{y}{1}=\frac{z+1}{1}$ is parallel to the plane
- A$2 x+y+z=2$
- B$2 x-y+z=2$
- C$x-y+2 z=2$
- Correct answerD$x-y-z=3$
Solution
Direction ratio's of given line $\equiv(2,1,1)$
From option (4), direction ratio's of plane
$\equiv(1,-1,-1)$
$\therefore 2 \times 1+1(-1)+1(-1)\left[l_1 l_2+m_1 m_2+n_1 n_2=0\right.$ if line and plane are parallel]
$2-1-1=0$
From option (4), direction ratio's of plane
$\equiv(1,-1,-1)$
$\therefore 2 \times 1+1(-1)+1(-1)\left[l_1 l_2+m_1 m_2+n_1 n_2=0\right.$ if line and plane are parallel]
$2-1-1=0$
Hence, the correct answer is option: 'D'.