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

If a,b,c are non-coplanar vectors r.a=r.b=r.c=0, show that r is a zero vector.

Open in App
Solution

Given
r.a=0;r.b=0;r.c=0
Let r is the point of intersection of three planes
r.ar.b=0r(a.b)=0...(i)
Similarly
r(a.c)=0...(ii)
r(a.b);r(a.c)
r=k(a.b)×(a.c)=k(a×aa×cb×a+b×c)
r=k(a.(a×b)+a.(b×c)+a.(c×a))
0=k(0+[abc])

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