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If vecx.veca=0vecx.vecb=0 and vecx.vecc=...

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

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The correct Answer is:
1
` 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.
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
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  8. A, B C and D are four points in a plane with position vectors, veca, v...

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  11. Let vecA, vecB and vecC be unit vectors such that vecA.vecB = vecA.vec...

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  17. If veca and vecb are vectors in space given by veca= (hati-2hatj)/sqrt...

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