CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A plane which contain the line yb+zc=1,x=0, and parallel to the line xazc=1,y=0. If 1a,1b,1c are the direction cosines of the a line l then distance of the plane from the origin is

Open in App
Solution

The equation of the line contained in the required plane
yb+zc=1,x=0yb12=12zc,x=0y12bb=z12cc=x0... (1)
Equation of the line which is parallel to plane
x12aa=z+12cc=y0... (2)
Equation of the plane containing the line (1) is
A(x0)+B(y12b)+C(z12c)=0hereA.0+B.bC.c=0... (3)
If the plane parallel to the plane, then
A.a+B.0+C.c=0... (4)
From equation (3) and (4)
Abc=Bac=Cab
putting the value of the A,B,C in the equation of the plane
bcxac(y12b)ab(z12c)=0xaybzc=1
Distance of the plane fron the origin is
|1|1a2+1b2+1c2=11a,1b,1c
are the direction cosines of a line
1a2+1b2+1c2=1

flag
Suggest Corrections
thumbs-up
4
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