(u+v−w)⋅(u×v−u×w−v×v+v×w) (u+v−w)⋅(u×v−u×w+v×w)=0u⋅(u×v) −0u.(u×w)+u.(v×w)+0v⋅(u×v)−v⋅(u×w) +0v⋅(v×w)−w⋅(u×v)+0w⋅(u×w)−0w⋅(u×w)=u⋅(v×w)−v⋅(u×w)−w⋅(u×v) =[uvw]+[vwu]−[wuv]=u.(v×w)
If u, v and w are three non-coplanar vectors, then ( u+ v- w) .( u- v) ×( v- w) equals
JEE Main 2003 — Mathematics Vectors & 3D Geometry
2003mcqmedium
If u,v and w are three non-coplanar vectors, then (u+v−w).(u−v)×(v−w) equals
Official previous-year question
Held on 30 Apr 2003 · Verified 6 Jul 2026.
Options
- A
3u.v×w
- B
0
- C
u⋅v×w
- D
u⋅w×v
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