Q84 / 180 · KCET 2014 · Mathematics

The line \( \frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5} \) is parallel to the plane

  • A
    \( 3 x+4 y+5 z=7 \)
  • B
    \( x+y+z=2 \)
  • C
    \( 2 x+3 y+4 z=0 \)
  • Correct answer
    D
    \( 2 x+y-2 z=0 \)

Solution

Given that, $\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5} \rightarrow(1)$ So, direction ratio's of line are $3,4,5$ Since, line and plane are parallel. So, normal to plane and line are perpendicular Now, $a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}=0$ for plane $2 x+y-2 z=0$ Now, $3(2)+4(1)-2(5)=0$ Hence, required equation is $2 x+y-2 z=0$

Hence, the correct answer is option: 'D'.

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