If `vecx.veca=0vecx.vecb=0 and vecx.vecc=0` for some non zero vector `vecx` then show that `[veca vecb vecc]=0`

Answer

1

Explanation

` vecX. vecA = 0 Rightarrow " either " vecA = 0 or vecX bot vecA`
` vecX.vecC =0 Rightarrow " either" vecC=0 vecX bot vecC`
In any of the three cases,
`vecA, vecB, vecC =0 Rightarrow [vecA vecB vecC] =0`
Otherwise if `vecX bot vecA, vecX bot vecB and vecX bot vecC` , then
`vecA, vecB and vecC` are coplanar. then
` [ vecA vecB vecC] =0`
Therefore, the statement is true.