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

Two systems of rectangular axis have the same origin. If a plane cuts them at distances a,b,c and a',b;c', respectively from the origin, then prove that 1a2+1b2+1c2=1a2+1b2+1c2.

Open in App
Solution

Consider OX,OY,OZ and ox,oy,oz are two system of rectangluar axes.

Let their corresponding equation of plane be xa+yb+zc=1 ...(i)
and xa+yb+zc=1 ...(ii)
Also, the length of perpendicular from origin to Eqs. (i) and (ii) must be same. 0a+0b+0c11a2+1b2+1c2=0a+0b+0c11a2+1b2+1c2=1a2+1b2+1c2=1a2+1b2+1c21a2+1b2+1c2=1a2+1b2+1c2


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Vector Addition
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon