Question

The line joining points $\left(1,1,2\right)$ and $\left(3,-2,1\right)$ meets the plane $3x+2y+z=6$ at the point

• A. $\left(1,1,2\right)$
• B. $\left(3,-2,1\right)$
• C. $\left(2,-3,1\right)$
• D. $\left(3,2,1\right)$

Answer 1

The correct option is B

$\left(3,-2,1\right)$

Calculate the point of contact.

The straight line joining the points $\left(1,1,2\right)\&\left(3,-2,1\right)$ is given as

$\frac{x-1}{2}=\frac{y-1}{-3}=\frac{z-2}{-1}=r$.

Then, the point is $\left(2r+1,1-3r,2-r\right)$ which lies on $3x+2y+z=6$.

$\begin{array}{rcl}3\left(2r+1\right)+2\left(1-3r\right)+2-r& =& 6\\ r& =& 1\end{array}$

So, the required point is

$$\begin{gathered} \left(2\times 1+1,1-3\times 1,2-1\right) \\ \left(3,-2,1\right) \end{gathered}$$

Hence, option $\left(B\right)$ is correct.