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

In R3, consider the planes P1:y=0 and P2:x+z=1. Let P3 be a plane, different from P1 and P2, which passes through the intersection of P1 and P2. If the distance of the point (0,1,0) from P3 is 1 and the distance of a point (α,β,γ) from P3 is 2, then which of the following relations is/are true?

A
2α+β+2γ+2=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
2αβ+2γ+4=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
2α+β2γ10=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
2αβ+2γ8=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct options are
B 2αβ+2γ+4=0
D 2αβ+2γ8=0
Equation of family of planes passing through P1 and P2 (plane P3) is given by: P2+λP1=0
x+λy+z1=0

The distance of the point (0,1,0) from P3 is 1.
|λ1|λ2+2=1
λ=12

Thus, the equation of the plane P3 is 2xy+2z2=0
Now, the distance of a point (α,β,γ) from P3 is 2.
|2αβ+2γ2|3=2
2αβ+2γ8=0 or 2αβ+2γ+4=0

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Application of Vectors - Planes
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon