Search any question & find its solution
Question:
Answered & Verified by Expert
The line $\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$ is parallel to the plane
Options:
Solution:
2740 Upvotes
Verified Answer
The correct answer is:
$2 x+y-2 z=0$
We know that, any line is parallel to the plane, then normal to the plane is perpendicular to the line.
Given, line is $\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$
So, DR's of line are $\langle 3,4,5\rangle$.
Let us consider the equation of plane be $2 x+y-2 z=0$ [from the given options]
Hence, DR's of a plane are $\langle 2,1,-2\rangle$.
Now, $3 \times 2+4 \times 1+5 \times(-2)=6+4-10$
$$
=10-10=0
$$
Option (d) is correct.
Given, line is $\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$
So, DR's of line are $\langle 3,4,5\rangle$.
Let us consider the equation of plane be $2 x+y-2 z=0$ [from the given options]
Hence, DR's of a plane are $\langle 2,1,-2\rangle$.
Now, $3 \times 2+4 \times 1+5 \times(-2)=6+4-10$
$$
=10-10=0
$$
Option (d) is correct.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.