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 xa−zc=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=0yb−12=12−zc,x=0⇒y−12bb=z−12c−c=x0... (1) Equation of the line which is parallel to plane x−12aa=z+12cc=y0... (2) Equation of the plane containing the line (1) is A(x−0)+B(y−12b)+C(z−12c)=0hereA.0+B.b−C.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=B−ac=C−ab putting the value of the A,B,C in the equation of the plane bcx−ac(y−12b)−ab(z−12c)=0xa−yb−zc=1 Distance of the plane fron the origin is |−1|√1a2+1b2+1c2=1∵1a,1b,1c are the direction cosines of a line ∴1a2+1b2+1c2=1

Suggest Corrections
4
Join BYJU'S Learning Program
Related Videos
Equation of a Plane: General Form and Point Normal Form
MATHEMATICS
Watch in App
Join BYJU'S Learning Program