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

If a plane meets the coordinate axes in A,B and C, such that the centroid of ΔABC is (1,2,4) then the perpendicular distance from origin to the plane is

A
12
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
1221
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
7
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
721
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 1221
Let the required equation of the plane be
xa+yb+zc=1(i)
Then,it meets the coordinate axes in
A(a,0,0),B(0,b,0) and C(0,0,c)
So, centroid ofΔABC=(a+0+03,0+b+03,0+0+c3)
G(a3,b3,c3)
a3=1,b3=2 and c3=4
a=3,b=6,c=12
Hence,the required equation of the plane is
x3+y6+z12=1
4x+2y+z=12
Now dividing the plane equation by 21, we have
x421+y221+z121=1221
On comparing with xcosα+ycosβ+zcosγ=P
we have P=1221

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Equation of a Plane Parallel to a Given Plane
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon