wiz-icon
MyQuestionIcon
MyQuestionIcon
4
You visited us 4 times! Enjoying our articles? Unlock Full Access!
Question

A variable plane moves so that the sum of reciprocal of its intercepts on the three coordinate axes is constant λ. It passes through a fixed point, which has coordinates:

A
(λ,λ,λ)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

(1λ,1λ,1λ)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
(λ,λ,λ)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

(1λ,1λ,1λ)

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

The correct option is B

(1λ,1λ,1λ)


Let the equation of the variable is xa+yb+zc=1 ...(1)

The intercept on the coordinate axes are a,b,c.

The sum of reciprocals of intercepts is constant λ, therefore

1a+1b+1c=λ(1/λ)a+(1/λ)b+(1/λ)c=1

(1λ,1λ,1λ) lies on the plane (1)

Hence, the vatiable plane (1) always passes through the fixed point (1λ,1λ,1λ)


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Circle and Point on the Plane
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon