The line x-2/3=y-3/4=z-4/5 is parallel to the plane

Correct Answer is : 2x + y - 2z = 0

Correct Answer is : 2x + y - 2z = 0

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KCET 2014 Math Solved Paper

Question : 24 of 60

Marks: +1, -0

The line

\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}

is parallel to the plane

Solution:

Given that,

\;\frac{x-2}{3}=\;\frac{y-3}{4}=\;\frac{z-4}{5}

→ (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_1a_2+b_1b_2+c_1c_2=0

for plane

2x+y-2z=0

Now,

3(2)+4(1)-2(5)=0

Hence, required equation is

2x+y-2z=0

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