Q114 / 200 · Manipal (MET) 2014 · Mathematics
The line joining the points $(1,1,2)$ and $(3,-2,1)$ meets the plane $3 x+2 y+z=6$ at the point
- A$(1,1,2)$
- Correct answerB$(3,-2,1)$
- C$(2,-3,1)$
- D$(3,2,1)$
Solution
The straight line joining the points $(1,1,2)$ and $(3,-2,1)$ is $\frac{x-1}{2}=\frac{y-1}{-3}=\frac{z-2}{-1}=r$(say)
$\therefore$ point is $(2 r+1,1-3 r, 2-r)$ which lies on $3 x+2 y+z=6$ $\therefore \quad 3(2 r+1)+2(1-3 r)+2-r=6$ $\Rightarrow \quad r=1$ So, required point is $(3,-2,1)$.
$\therefore$ point is $(2 r+1,1-3 r, 2-r)$ which lies on $3 x+2 y+z=6$ $\therefore \quad 3(2 r+1)+2(1-3 r)+2-r=6$ $\Rightarrow \quad r=1$ So, required point is $(3,-2,1)$.
Hence, the correct answer is option: 'B'.