Question

The coordinate of the point of intersection of the line $\frac{[x-1]}{1}=\frac{[y+2]}{3}=\frac{[z-2]}{-2}$ with the plane $3x+4y+5z-25=0$ is

• A. $(5,10,6)$
• B. $(10,5,6)$
• C. $(5,5,-6)$
• D. $(5,10,-6)$

Answer 1

The correct option is D

$(5,10,-6)$

Explanation for the correct option:

Finding the point of intersection

Given equation of line,

$\frac{[x-1]}{1}=\frac{[y+2]}{3}=\frac{[z-2]}{-2}$

And equation of plane

$3x+4y+5z-25=0...\left(i\right)$

Now consider,

$\frac{[x-1]}{1}=\frac{[y+2]}{3}=\frac{[z-2]}{-2}=r$

$\Rightarrow x=r+1,y=3r–2,z=–2r+2...\left(ii\right)$

Substituting these values of $x,y\&z$ in $\left(i\right)$

$$\begin{gathered} \Rightarrow 3(r+1)+4(3r–2)+5(-2r+2)–25=0 \\ \Rightarrow 5r–20=0 \\ \Rightarrow r=\frac{20}{5} \\ \Rightarrow r=4 \end{gathered}$$

Therefore, from (ii)

$x=5,y=10,z=–6$

Thus the required point is $(5,10,–6)$

Hence, option (D) is the correct answer.