if a,b,c, are three non co planar vectors such that d.a=d.b=d.c=0(where d.a represent scalar product )then show that d is null vector.

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- September 28th 2012, 11:36 AMayushdadhwalnull vector
if a,b,c, are three non co planar vectors such that d.a=d.b=d.c=0(where d.a represent scalar product )then show that d is null vector.

- September 28th 2012, 11:43 AMTheEmptySetRe: null vector
- September 28th 2012, 12:27 PMHallsofIvyRe: null vector
**If**you are working in three dimensions, then a, b, and c must form a basis (otherwise they would not be non-planar) so d can be written as d= xa+ yb+ zc for numbers x, y, and z. Take the dot product of d with xa+ yb+ zc.