wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A plane which passes through the point (3,2,0) and the line x-31=y-75=z-44 is


A

xy+z=1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B

x+y+z=5

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

x+2y-z=0

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

2x-y+z=5

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A

xy+z=1


Explanation for correct option:

Step1. Expressing the given data according to the question.

Given,

Equation of line, x-31=y-75=z-44

A plane passing through the point (3,2,0) & line.

Step2. Writing general formulae of a plane

Let the equation of plane passing through (3,2,0) is given by

a(x-3)+b(y-2)+c(z-0)=0....(i)

Step3. Finding equation plane.

The line has direction ratio (1,5,4)

If the equation of plane contains this , it should pass from (3,7,4) & parallel to (1,5,4)

a(3-1)+b(7-5)+c(4-4)=0

2a+2b=0

a+b=0...(ii)

And a+5b+4c=0...(iii)

On solving equation (ii)&(iii) we get,

a=cb=-c

Therefore equation of plane is

c(x-3)-c(y-2)+cz=0 From (i)

x-y+z=1

Hence correct option is (A).


flag
Suggest Corrections
thumbs-up
5
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Drawing Tangents to a Circle
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon