wiz-icon
MyQuestionIcon
MyQuestionIcon
3
You visited us 3 times! Enjoying our articles? Unlock Full Access!
Question

If the line x23=y+12=z11 intersects the plane 2x+3yz+13=0 at a point P and the plane 3x+y+4z=16 at a point Q, then PQ is equal to :

A
14
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
214
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
14
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
27
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 214
Given line x23=y+12=z11= λ(let)
Therefore general point of line:
(3λ+2, 2λ1, 1λ) which intersect the plane 2x+3yz+13=0 at a point P
then 2(3λ+2)+3(2λ1)(1λ)+13=0λ=1
So, point P(1,3, 2)
Also line intersect the plane 3x+y+4z=16 at a point Q
therefore 3(3λ+2)+(2λ1)+4(1λ)=16λ=1
So, point Q(5,1,0)
therefore PQ=(5+1)2+(1+3)2+(02)2
PQ=214

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Angle between a Plane and a Line
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon