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

Let P be the plane containing the line L1:y+z=2, x=0 and is parallel to the line L2:xz=2,y=0. If the distance of the plane P from the origin is d units, then the value of 3d2 is

Open in App
Solution

Equation of L1 is
x00=y11=z11
Similarly, equation of L2 is x11=y00=z+11

So, equation of any plane through line L1 is ax+b(y1)+c(z1)=0 (1)
where a×0+b×1+c×(1)=0 (2)
Also, the plane (1) is parallel to the line L2.
So a×1+b×0+c×1=0 (3)

From (2) and (3), we get
a1=b1=c1

So, the required plane P, is
1(x0)1(y1)1(z1)=0
xyz+2=0

Distance from the origin to the plane xyz+2=0 is
d=21+1+1=23
Hence, 3d2=4


flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Equation of a Plane: General Form and Point Normal Form
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon